ddrg/math_formulas · Datasets at Hugging Face

id int64 -30,985 55.9k	text stringlengths 5 437k
-4,641	\frac{2 \cdot x + 13}{20 + x \cdot x + 9 \cdot x} = \frac{1}{x + 4} \cdot 5 - \frac{1}{5 + x} \cdot 3
51,623	2*7 + 6 = 20
26,913	1 - \dfrac{1}{y2 + 1}4 = \dfrac{1}{1 + 2y}(2y + 3(-1))
5,040	-k! + (1 + k)! = kk!
-5,233	65.1 \cdot 10^3 = 65.1 \cdot 10^{-2 + 5}
7,495	a - e + x = a - -x + e
34,632	\left(-1\right)^p = \cos{\pi\cdot p} + i\cdot \sin{\pi\cdot p} \approx 1 + i\cdot \pi\cdot p
-8,825	\pi\cdot 96 = 64\cdot \pi + \pi\cdot 16 + 16\cdot \pi
28,732	\frac{(-1) + s^2}{s + (-1)} = s + 1
18,514	\sin{a} \cdot \cos{h} + \sin{h} \cdot \cos{a} = \sin(h + a)
-17,556	47 = 7\left(-1\right) + 54
28,365	(a - b)^2 = (a - b) \cdot (a - b) = a \cdot a - 2 \cdot a \cdot b + b^2
-28,758	1/3 - \tfrac{4}{y3 + 6} = 1/3 - \frac{4\frac13}{y + 2}
-27,691	\frac{d}{dx} (-5\cdot \sin\left(x\right)) = -\cos(x)\cdot 5
-6,180	\frac{1}{(y + 3\cdot (-1))\cdot (5 + y)}\cdot (5\cdot (3\cdot \left(-1\right) + y) - 3\cdot (y + 5) + 4) = \frac{1}{\left(y + 5\right)\cdot \left(y + 3\cdot \left(-1\right)\right)}\cdot (-15 + y\cdot 5) - \frac{1}{(y + 3\cdot (-1))\cdot (5 + y)}\cdot (15 + y\cdot 3) + \frac{4}{(y + 5)\cdot (y + 3\cdot (-1))}
12,589	\frac26 = 1/6 + 1/6
1,458	2^x - 2^{2 \cdot (-1) + x} \cdot \left((-1) + x\right) + 2^{x + 4 \cdot (-1)} \cdot (2 \cdot (-1) + x) \cdot (3 \cdot (-1) + x)/2! - \dotsm = 1 + x
8,111	{n \choose x + 1} + {n \choose x} = {1 + n \choose x + 1}
-10,761	\frac{1}{2 + r}4*\frac55 = \tfrac{20}{10 + 5r}
17,691	1 + x + x \cdot x + \dotsm = e^x
37,586	150 = 3 \cdot 5^2 \cdot 2
37,583	l = l^2/l
20,989	5\times n + n + n\times 3 = 9\times n
28,919	\frac{1}{x + (-1)} = \frac{1}{x \cdot (-\frac{1}{x} + 1)}
-5,657	\frac{2}{n^2 - 12 \cdot n + 32} = \frac{2}{\left(8 \cdot (-1) + n\right) \cdot (4 \cdot (-1) + n)}
10,648	\left(\frac{1 + 2\times x}{2 + x} = x\Longrightarrow x \times x = 1\right)\Longrightarrow x = 1
17,266	\frac{1}{c} \cdot b \cdot h = h \cdot b/c
49,325	\frac{\partial}{\partial x} \sum_{n=0}^\infty x^n = \sum_{n=0}^\infty \frac{\partial}{\partial x} x^n = \sum_{n=0}^\infty n\cdot x^{n + (-1)}
-10,456	\frac22 \cdot (-\tfrac{1}{5 \cdot q^2} \cdot (q + 7 \cdot (-1))) = -\frac{1}{q^2 \cdot 10} \cdot \left(2 \cdot q + 14 \cdot (-1)\right)
-12,519	40 = 90 + 50\cdot \left(-1\right)
-29,570	-y = -y^2/y
-29,347	(-b + h) (h + b) = -b b + h^2
26,939	y^2 - 4y = \left(2(-1) + y\right) \cdot \left(2(-1) + y\right) + 4(-1)
-20,573	\dfrac{1}{-3}\cdot (x + 1)\cdot 8/8 = (x\cdot 8 + 8)/\left(-24\right)
6,472	fh(fh)^i = fh(fh)^i
-3,318	\sqrt{3} + \sqrt{3} \cdot \sqrt{9} = \sqrt{3} + \sqrt{3} \cdot 3
4,769	2 \cdot 2^k = 2^{k+1}
-26,649	-25q^2 + s s4 = (s2)^2 - (5*q)^2
-11,528	-37 - 5\cdot i = -5\cdot i - 12 + 25\cdot \left(-1\right)
-4,241	30/18\cdot \dfrac{n^2}{n^2} = \frac{1}{n^2\cdot 18}\cdot n^2\cdot 30
2,403	a^2 + 4 + a \cdot 4 = (2 + a) \cdot (2 + a)
24,489	20 + 6 \cdot (-1) = 14
-10,658	21/(3\times r) = 7/r\times 3/3
7,552	d/h\Longrightarrow d/h
12,955	x^4-16=(x-2)(x+2)(x^2+4)
-20,054	\dfrac{1}{(-1) + x} \cdot (2 \cdot x + 9) \cdot \frac{9}{9} = \frac{81 + 18 \cdot x}{9 \cdot x + 9 \cdot \left(-1\right)}
22,770	3 \cdot 3 + 3\cdot (-1) + (-1) = 9 + 3\cdot \left(-1\right) + (-1) = 0
17,183	\frac{(2\cdot m)!}{2^m\cdot m!} = 3\cdot 5\cdot \dotsm\cdot (m\cdot 2 + (-1))
21,565	\left( 11, 60, 61\right) = ( -5^2 + 6^2, 60, 6^2 + 5 \cdot 5)
20,333	1/3 = \frac{1}{72}*24
-5,899	\frac{1}{4\times (n + 6\times (-1))}\times 2 = \frac{2}{4\times n + 24\times (-1)}
11,630	\sum_{m=1}^h \left(m^2 + (-1)\right) = \sum_{m=1}^h (m + (-1)) (1 + m)
4,817	b = a \implies b^4 = a^4
13,342	A^n \times C = A^n \times C
27,232	h\cdot d\cdot g = d\cdot h\cdot g
-2,916	\sqrt{11} = (4 + 5 \cdot (-1) + 2) \cdot \sqrt{11}
-23,408	\tfrac35 = \dfrac34\times \frac{4}{5}
30,254	5 \cdot \left(-\sqrt{1} + \sqrt{2}\right) = 5 \cdot (\sqrt{2} + \left(-1\right))
16,614	\frac{1}{k}(k + 2) = \frac1k(k + 1)\frac{1}{k + 1}\left(k + 2\right)
-20,639	\frac{1}{4} 1 = \frac{1}{12 (-1) - r \cdot 4} \left(-r + 3 (-1)\right)
19,135	0 = Z + 2x^{Z + 2} = Z + 2x^2 x^Z
24,145	a + b = -8 rightarrow -2 = -b + a
-20,709	-\dfrac65 \cdot \frac{9 \cdot s + 4 \cdot (-1)}{s \cdot 9 + 4 \cdot (-1)} = \frac{-54 \cdot s + 24}{s \cdot 45 + 20 \cdot \left(-1\right)}
-12,032	5/8 = t/(20\pi)20*\pi = t
-22,222	(y + 4)\cdot \left(y + 5\right) = 20 + y^2 + 9\cdot y
-28,178	\frac{\text{d}}{\text{d}y} \csc{y} = -\cot{y}\cdot \csc{y}
8,072	(\|z_1\| + 1) \|z_2\| = \|z_1\| (\|z_2\| + 1) \implies \|z_1\| = \|z_2\|
23,794	(-1)^{2 + k} = (-1)^k
36,805	-15 = 3 \cdot (-5)
-6,341	\dfrac{4}{y \cdot y - 7 \cdot y + 30 \cdot (-1)} = \frac{4}{(10 \cdot (-1) + y) \cdot (y + 3)}
8,891	z^2 + 5z + 6 = \left(z + 3\right) \left(z + 3\right) - z + 3
-22,799	\frac{22}{99} = \dfrac{211}{911}
18,842	x + 9 \cdot (-1) = \left(\sqrt{x} + 3 \cdot (-1)\right) \cdot (\sqrt{x} + 3)
12,524	3240 = 3\cdot 3\cdot 3\cdot {10 \choose 7}
-940	-\dfrac{1}{4}*7 = -7/4
24,511	\sin{\frac37 \cdot \pi} = \sin{4 \cdot \pi/7}
19,978	6 \cdot (-1) + 15 + 3 \cdot (-1) = 6
-7,109	1/22 = \frac{3}{12} \cdot 2/11
-4,423	\frac{3x + 9}{5(-1) + x^2 + x*4} = \tfrac{2}{(-1) + x} + \frac{1}{5 + x}
12,510	\left(\frac13 \cdot 2\right)^2 = \frac{4}{9}
-20,943	\left(30\cdot x + 40\right)/(40\cdot x) = 5/5\cdot \frac{6\cdot x + 8}{8\cdot x}
26,406	3/5*2/7 = \frac{6}{35}
25,008	(5^{1 / 2} + 1)\cdot \left(5^{\frac{1}{2}} + (-1)\right) = 4
-593	-\pi\cdot 4 + \pi\cdot \frac{35}{6} = \pi\cdot \frac{11}{6}
-7,528	c^2 - y^2 = \left(c + y\right) \cdot (c - y)
-22,316	(n + 3) (n + 8) = 24 + n^2 + 11 n
-2,733	96^{1/2} - 54^{1/2} + 6^{1/2} = \left(166\right)^{1/2} - (96)^{1/2} + 6^{1/2}
2,621	10 \cdot 10^2 - 5^3 = (10 + 5\cdot (-1))\cdot (5\cdot (-1) + 10)\cdot (2^2\cdot 5 + 2\cdot 5 + 5)
28,611	(x^6)^{1/2} = \|(x^6)^{\frac12}\| = \|x^3\|
35,005	\frac{\partial}{\partial x} (f \cdot h) = h \cdot \frac{\mathrm{d}f}{\mathrm{d}x}
39,971	1 + \left(-1\right)^1 = 0
5,875	j = e^{j \theta} = \cos{\theta} + j \sin{\theta}
-20,004	\frac{z72}{40 (-1) - 56 z} = 8/8 \frac{z9}{-7z + 5(-1)}1
18,944	s^2 + 2\cdot s + 4\cdot \left(-1\right) = 0 rightarrow -1 \pm \sqrt{5} = s
14,251	144^{\sin^2{x}} = \left(12^2\right)^{\sin^2{x}} = 12^{\sin^2{x}} \cdot 12^{\sin^2{x}}
21,757	y \cdot y = 0 + y \cdot y + y\cdot 0
7,577	\frac{2z^2 + z}{z^2 + 1} = 1 + \frac{z^2 + z + (-1)}{z z + 1} = 1 + \frac{1}{2(z z + 1)}(2z * z + 2z + 2(-1))
36,869	198=202-4
3,763	2/7 = \frac17\cdot 3\cdot \frac{4}{6}
4,420	-\int_1^0 {12 z}\,dz = \int\limits_0^1 {12 z}\,dz

-4,641

\frac{2 \cdot x + 13}{20 + x \cdot x + 9 \cdot x} = \frac{1}{x + 4} \cdot 5 - \frac{1}{5 + x} \cdot 3

51,623

2*7 + 6 = 20

26,913

1 - \dfrac{1}{y*2 + 1}*4 = \dfrac{1}{1 + 2*y}*(2*y + 3*(-1))

5,040

-k! + (1 + k)! = kk!

-5,233

65.1 \cdot 10^3 = 65.1 \cdot 10^{-2 + 5}

7,495

a - e + x = a - -x + e

34,632

\left(-1\right)^p = \cos{\pi\cdot p} + i\cdot \sin{\pi\cdot p} \approx 1 + i\cdot \pi\cdot p

-8,825

\pi\cdot 96 = 64\cdot \pi + \pi\cdot 16 + 16\cdot \pi

28,732

\frac{(-1) + s^2}{s + (-1)} = s + 1

18,514

\sin{a} \cdot \cos{h} + \sin{h} \cdot \cos{a} = \sin(h + a)

-17,556

47 = 7\left(-1\right) + 54

28,365

(a - b)^2 = (a - b) \cdot (a - b) = a \cdot a - 2 \cdot a \cdot b + b^2

-28,758

1/3 - \tfrac{4}{y*3 + 6} = 1/3 - \frac{4*\frac13}{y + 2}

-27,691

\frac{d}{dx} (-5\cdot \sin\left(x\right)) = -\cos(x)\cdot 5

-6,180

\frac{1}{(y + 3\cdot (-1))\cdot (5 + y)}\cdot (5\cdot (3\cdot \left(-1\right) + y) - 3\cdot (y + 5) + 4) = \frac{1}{\left(y + 5\right)\cdot \left(y + 3\cdot \left(-1\right)\right)}\cdot (-15 + y\cdot 5) - \frac{1}{(y + 3\cdot (-1))\cdot (5 + y)}\cdot (15 + y\cdot 3) + \frac{4}{(y + 5)\cdot (y + 3\cdot (-1))}

12,589

\frac26 = 1/6 + 1/6

1,458

2^x - 2^{2 \cdot (-1) + x} \cdot \left((-1) + x\right) + 2^{x + 4 \cdot (-1)} \cdot (2 \cdot (-1) + x) \cdot (3 \cdot (-1) + x)/2! - \dotsm = 1 + x

8,111

{n \choose x + 1} + {n \choose x} = {1 + n \choose x + 1}

-10,761

\frac{1}{2 + r}4*\frac55 = \tfrac{20}{10 + 5r}

17,691

1 + x + x \cdot x + \dotsm = e^x

37,586

150 = 3 \cdot 5^2 \cdot 2

37,583

l = l^2/l

20,989

5\times n + n + n\times 3 = 9\times n

28,919

\frac{1}{x + (-1)} = \frac{1}{x \cdot (-\frac{1}{x} + 1)}

-5,657

\frac{2}{n^2 - 12 \cdot n + 32} = \frac{2}{\left(8 \cdot (-1) + n\right) \cdot (4 \cdot (-1) + n)}

10,648

\left(\frac{1 + 2\times x}{2 + x} = x\Longrightarrow x \times x = 1\right)\Longrightarrow x = 1

17,266

\frac{1}{c} \cdot b \cdot h = h \cdot b/c

49,325

\frac{\partial}{\partial x} \sum_{n=0}^\infty x^n = \sum_{n=0}^\infty \frac{\partial}{\partial x} x^n = \sum_{n=0}^\infty n\cdot x^{n + (-1)}

-10,456

\frac22 \cdot (-\tfrac{1}{5 \cdot q^2} \cdot (q + 7 \cdot (-1))) = -\frac{1}{q^2 \cdot 10} \cdot \left(2 \cdot q + 14 \cdot (-1)\right)

-12,519

40 = 90 + 50\cdot \left(-1\right)

-29,570

-y = -y^2/y

-29,347

(-b + h) (h + b) = -b b + h^2

26,939

y^2 - 4y = \left(2(-1) + y\right) \cdot \left(2(-1) + y\right) + 4(-1)

-20,573

\dfrac{1}{-3}\cdot (x + 1)\cdot 8/8 = (x\cdot 8 + 8)/\left(-24\right)

6,472

f*h*(f*h)^i = f*h*(f*h)^i

-3,318

\sqrt{3} + \sqrt{3} \cdot \sqrt{9} = \sqrt{3} + \sqrt{3} \cdot 3

4,769

2 \cdot 2^k = 2^{k+1}

-26,649

-25*q^2 + s * s*4 = (s*2)^2 - (5*q)^2

-11,528

-37 - 5\cdot i = -5\cdot i - 12 + 25\cdot \left(-1\right)

-4,241

30/18\cdot \dfrac{n^2}{n^2} = \frac{1}{n^2\cdot 18}\cdot n^2\cdot 30

2,403

a^2 + 4 + a \cdot 4 = (2 + a) \cdot (2 + a)

24,489

20 + 6 \cdot (-1) = 14

-10,658

21/(3\times r) = 7/r\times 3/3

7,552

d/h\Longrightarrow d/h

12,955

x^4-16=(x-2)(x+2)(x^2+4)

-20,054

\dfrac{1}{(-1) + x} \cdot (2 \cdot x + 9) \cdot \frac{9}{9} = \frac{81 + 18 \cdot x}{9 \cdot x + 9 \cdot \left(-1\right)}

22,770

3 \cdot 3 + 3\cdot (-1) + (-1) = 9 + 3\cdot \left(-1\right) + (-1) = 0

17,183

\frac{(2\cdot m)!}{2^m\cdot m!} = 3\cdot 5\cdot \dotsm\cdot (m\cdot 2 + (-1))

21,565

\left( 11, 60, 61\right) = ( -5^2 + 6^2, 60, 6^2 + 5 \cdot 5)

20,333

1/3 = \frac{1}{72}*24

-5,899

\frac{1}{4\times (n + 6\times (-1))}\times 2 = \frac{2}{4\times n + 24\times (-1)}

11,630

\sum_{m=1}^h \left(m^2 + (-1)\right) = \sum_{m=1}^h (m + (-1)) (1 + m)

4,817

b = a \implies b^4 = a^4

13,342

A^n \times C = A^n \times C

27,232

h\cdot d\cdot g = d\cdot h\cdot g

-2,916

\sqrt{11} = (4 + 5 \cdot (-1) + 2) \cdot \sqrt{11}

-23,408

\tfrac35 = \dfrac34\times \frac{4}{5}

30,254

5 \cdot \left(-\sqrt{1} + \sqrt{2}\right) = 5 \cdot (\sqrt{2} + \left(-1\right))

16,614

\frac{1}{k}*(k + 2) = \frac1k*(k + 1)*\frac{1}{k + 1}*\left(k + 2\right)

-20,639

\frac{1}{4} 1 = \frac{1}{12 (-1) - r \cdot 4} \left(-r + 3 (-1)\right)

19,135

0 = Z + 2x^{Z + 2} = Z + 2x^2 x^Z

24,145

a + b = -8 rightarrow -2 = -b + a

-20,709

-\dfrac65 \cdot \frac{9 \cdot s + 4 \cdot (-1)}{s \cdot 9 + 4 \cdot (-1)} = \frac{-54 \cdot s + 24}{s \cdot 45 + 20 \cdot \left(-1\right)}

-12,032

5/8 = t/(20*\pi)*20*\pi = t

-22,222

(y + 4)\cdot \left(y + 5\right) = 20 + y^2 + 9\cdot y

-28,178

\frac{\text{d}}{\text{d}y} \csc{y} = -\cot{y}\cdot \csc{y}

8,072

(|z_1| + 1) |z_2| = |z_1| (|z_2| + 1) \implies |z_1| = |z_2|

23,794

(-1)^{2 + k} = (-1)^k

36,805

-15 = 3 \cdot (-5)

-6,341

\dfrac{4}{y \cdot y - 7 \cdot y + 30 \cdot (-1)} = \frac{4}{(10 \cdot (-1) + y) \cdot (y + 3)}

8,891

z^2 + 5*z + 6 = \left(z + 3\right) * \left(z + 3\right) - z + 3

-22,799

\frac{22}{99} = \dfrac{2*11}{9*11}

18,842

x + 9 \cdot (-1) = \left(\sqrt{x} + 3 \cdot (-1)\right) \cdot (\sqrt{x} + 3)

12,524

3240 = 3\cdot 3\cdot 3\cdot {10 \choose 7}

-940

-\dfrac{1}{4}*7 = -7/4

24,511

\sin{\frac37 \cdot \pi} = \sin{4 \cdot \pi/7}

19,978

6 \cdot (-1) + 15 + 3 \cdot (-1) = 6

-7,109

1/22 = \frac{3}{12} \cdot 2/11

-4,423

\frac{3*x + 9}{5*(-1) + x^2 + x*4} = \tfrac{2}{(-1) + x} + \frac{1}{5 + x}

12,510

\left(\frac13 \cdot 2\right)^2 = \frac{4}{9}

-20,943

\left(30\cdot x + 40\right)/(40\cdot x) = 5/5\cdot \frac{6\cdot x + 8}{8\cdot x}

26,406

3/5*2/7 = \frac{6}{35}

25,008

(5^{1 / 2} + 1)\cdot \left(5^{\frac{1}{2}} + (-1)\right) = 4

-593

-\pi\cdot 4 + \pi\cdot \frac{35}{6} = \pi\cdot \frac{11}{6}

-7,528

c^2 - y^2 = \left(c + y\right) \cdot (c - y)

-22,316

(n + 3) (n + 8) = 24 + n^2 + 11 n

-2,733

96^{1/2} - 54^{1/2} + 6^{1/2} = \left(16*6\right)^{1/2} - (9*6)^{1/2} + 6^{1/2}

2,621

10 \cdot 10^2 - 5^3 = (10 + 5\cdot (-1))\cdot (5\cdot (-1) + 10)\cdot (2^2\cdot 5 + 2\cdot 5 + 5)

28,611

(x^6)^{1/2} = |(x^6)^{\frac12}| = |x^3|

35,005

\frac{\partial}{\partial x} (f \cdot h) = h \cdot \frac{\mathrm{d}f}{\mathrm{d}x}

39,971

1 + \left(-1\right)^1 = 0

5,875

j = e^{j \theta} = \cos{\theta} + j \sin{\theta}

-20,004

\frac{z*72}{40 (-1) - 56 z} = 8/8 \frac{z*9}{-7z + 5(-1)}1

18,944

s^2 + 2\cdot s + 4\cdot \left(-1\right) = 0 rightarrow -1 \pm \sqrt{5} = s

14,251

144^{\sin^2{x}} = \left(12^2\right)^{\sin^2{x}} = 12^{\sin^2{x}} \cdot 12^{\sin^2{x}}

21,757

y \cdot y = 0 + y \cdot y + y\cdot 0

7,577

\frac{2*z^2 + z}{z^2 + 1} = 1 + \frac{z^2 + z + (-1)}{z * z + 1} = 1 + \frac{1}{2*(z * z + 1)}*(2*z * z + 2*z + 2*(-1))

36,869

198=202-4

3,763

2/7 = \frac17\cdot 3\cdot \frac{4}{6}

4,420

-\int_1^0 {1*2 z}\,dz = \int\limits_0^1 {1*2 z}\,dz