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ddrg
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math_formulas

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int64
-30,985
55.9k
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38,973
x\cdot 2 = \frac{3 \pi}{4} \Rightarrow x = \frac{1}{8} \pi\cdot 3
-15,321
\tfrac{1}{\frac{q^{10}}{n^2} n^2} = \tfrac{1}{n^2*\left(\frac{q^5}{n}\right)^2}
1,912
\frac{l!}{(l - v)!\cdot v!} = {l \choose v}
-10,526
\frac{1 + p}{p^3 \cdot 4} \cdot \frac{1}{4}4 = \frac{4p + 4}{16 p^3}
-7,509
\tfrac14 \cdot 17 = 34/8
11,866
x\times \lambda_g = x\times \lambda_g
3,923
w \in \mathbb{R}, x - y = w\Longrightarrow x = w + y
21,812
4(-1) + (2(-1) + z) * (2(-1) + z) = z^2 - 4z
16,911
3/5 \cdot \frac{1}{4} \cdot 2 = \tfrac{1}{10} \cdot 3
18
1^2+1^2=1*2\implies 2=2
-9,119
\dfrac{1}{100}*74.8 = 74.8\%
-20,482
\frac{-n \cdot 10 + 4 \cdot (-1)}{n \cdot 70 + 28} = \frac{1}{4 + 10 \cdot n} \cdot (10 \cdot n + 4) \cdot (-1/7)
9,064
\eta = 1/\eta = 1/\eta\cdot L^{-T}/L = \eta\cdot L^{-T}/L
-30,701
21\times (-1) - x\times 14 = -7\times (2\times x + 3)
27,985
|z + (-1)| = |1 - z| \geq |1| - |z| = 1 - |z| rightarrow |z| \geq \frac{3}{4}
13,408
\frac{b}{g} = b/g
8,046
1 + 8 \cdot \frac19 \cdot ((-1) + 10^{l + 1}) = \frac{1}{9} \cdot (8 \cdot 10^{l + 1} + 1)
7,110
1 - \frac{1}{1 + x^n} = \frac{1}{x^n + 1}*x^n
24,234
\frac{1}{(d + x) \cdot (x + h)} = \frac{1}{h - d} \cdot (-\frac{1}{h + x} + \frac{1}{d + x})
4,606
y*T/I = y*T/I
15,053
\dfrac{a^b}{a^d} = a^{-d + b}
-509
\frac{11}{12} \cdot \pi = -26 \cdot \pi + \pi \cdot 323/12
15,737
x^{3/2} = x^{\frac{1}{2}}*x
32,079
\dotsm^2 = \dotsm\cdot \dotsm
49,740
54/6=9
-2,690
25^{\frac{1}{2}}\cdot 7^{\frac{1}{2}} + 7^{\frac{1}{2}} = 5\cdot 7^{1 / 2} + 7^{\frac{1}{2}}
28,875
5/2 - \frac25 = \frac{21}{10}
-30,073
14 \cdot y + 6 \cdot y^5 + y \cdot y \cdot y \cdot 12 = \frac{\mathrm{d}}{\mathrm{d}y} \left(7 \cdot y^2 + y^6 + 3 \cdot y^4\right)
23,865
\cos^k{z} = \cos^k{z}
19,765
3 (-1) + 7 = 4
875
2 = A/x = \frac{A}{x \cdot U} \cdot \dfrac{U}{x} \cdot x = \dfrac{1}{x \cdot U} \cdot A \cdot |U|
-2,340
\frac{6}{11} - 4/11 = \frac{1}{11}*2
30,293
1365 = 19^2\cdot 3 + 16\cdot 19^0 + 14\cdot 19^1
21,618
\frac{y}{y + (-1)} = \frac{1}{y + \left(-1\right)}\cdot (y + (-1) + 1) = 1 + \frac{1}{y + (-1)}
10,361
x^2 + 3 - x^2 + 2\cdot x + 1 = x^2 - x^2 - 2\cdot x + 3 + \left(-1\right) = -2\cdot x + 2 = -2\cdot (x + (-1))
15,272
0 = B_4 - B_1*2 - 3*\frac{1}{5}*(2*B_1 - B_2) \Rightarrow B_4*5 - B_1*16 + 3*B_2 = 0
-20,058
\dfrac{1}{k + 9} \left(-6 k + 6 (-1)\right)*9/9 = \frac{1}{81 + 9 k} (-54 k + 54 (-1))
17,141
-h + e - f = e - f - h
18,100
\frac{y}{y^4 + 9} = \dfrac{1/9 \cdot y}{1 - -\frac{y^4}{9}}
19,466
P(A) = P(A)
23,800
\left\lceil{\frac{5}{(30/7)^{1/2}}}\right\rceil = 3
1,611
1/10 = \frac{8}{9} \cdot 9/10/8
-23,609
1/5 = 1/5 \cdot 2/2
-1,469
-\frac95*(-\dfrac79) = \frac{\frac19*(-7)}{(-5)*1/9}
-2,120
11/12 \times \pi + \tfrac{1}{12} \times 23 \times \pi = \frac{17}{6} \times \pi
-22,710
\tfrac{1}{49}\cdot 28 = 7\cdot 4/(7\cdot 7)
21,175
\frac{1}{g_1 g_2} = 1/(g_1 g_2)
23,039
z^2 + \frac{1}{z^2} = 2 (-1) + (\frac1z + z) (\frac1z + z)
8,890
mc = mc
32,760
b*g = (\sqrt{g*b})^2
24,690
\frac16 + 1/6 = \frac{1}{3}
17,222
\dfrac{1}{2} + 1/4 + \dfrac18 + \ldots + \frac{1}{2^k} = \dfrac{1}{2^k}*((-1) + 2^k)
-7,563
\frac{-i\cdot 9 + 9}{3 + 3\cdot i}\cdot \frac{3 - i\cdot 3}{-3\cdot i + 3} = \frac{9 - i\cdot 9}{3 + 3\cdot i}
-1,632
\frac{3}{2}\cdot \pi = \pi + \frac{1}{2}\cdot \pi
12,111
\sin\left(\pi - e - h - c\right) = \sin(e + h + c) = \sin\left(e + h\right) \cos(c) + \cos(e + h) \sin(c)
15,026
0 < \tfrac{e^{-1/z}}{z} = \frac{1}{z\cdot e^{\frac1z}} < 2\cdot z
2,088
(x + 1)\cdot \left(1 + x \cdot x - x\right) = 1 + x^3
23,102
s^2*s = s^3
35,767
10 + 6\cdot \sqrt{3} = 1 + 3\cdot \sqrt{3} + 9 + 3\cdot \sqrt{3} = 1 + 3\cdot \sqrt{3} + 3\cdot (\sqrt{3})^2 + (\sqrt{3})^3 = \left(1 + \sqrt{3}\right)^3
-11,580
-6 i - 9 + 1 = -8 - i*6
11,655
(-c a + a^2 + d d + c c - d a - c d) \left(a + d + c\right) = a^3 + d d d + c^3 - 3 d c a
-20,243
8/5 \dfrac{8 + 6q}{6q + 8} = \frac{64 + 48 q}{q\cdot 30 + 40}
21,537
2*\left(-b + a\right) = 2*a - 2*b
6,992
\dfrac{30}{12^5}\cdot 66 = 55/6912
16,569
\sin(\pi - t\cdot \pi) = \sin{\pi\cdot t}
-18,960
\frac192 = Z_t/(81 \pi)\cdot 81 \pi = Z_t
10,475
\cos(x \cdot t) = \cos(-t \cdot x)
976
a a + a b*2 + b^2 = (b + a) (b + a)
15,713
X \cdot X \cdot X - t^2 \cdot t = (X - t)\cdot (X^2 + t\cdot X + t^2)
4,795
-1.3 = (j + 10\cdot (-1))/2 \Rightarrow j = 7.4
33,797
5 \cdot 5 + 5^2 = 7^2 + 1 \cdot 1
4,195
\overline{e^{m\cdot x + i\cdot p}} = \overline{e^{m\cdot x}\cdot e^{i\cdot p}} = e^{m\cdot x}\cdot e^{-i\cdot p} = e^{m\cdot x - i\cdot p}
2,030
\frac{1}{x + 1}(x^2 + 2x + 2) = x + 1 + \frac{1}{1 + x}
-4,231
40/120\cdot y/y = 40\cdot y/\left(120\cdot y\right)
9,763
1/\left(g\cdot x\right) = 1/(x\cdot g)
-16,412
3\cdot (16\cdot 3)^{\frac{1}{2}} = 3\cdot 48^{1 / 2}
5,562
\frac{1}{4323} = 4322 \cdot 1/4323/4322
26,760
\dfrac{x}{c_3}\times 1/c_2\times \ldots^{-1}/A = x\times |c_2\times |c_3|\times \ldots|\times A
16,285
l = \dfrac{l!}{\left(\left(-1\right) + l\right)!}
-20,586
\frac{1}{3} \times 8 \times \frac{1}{2 + 9 \times n} \times \left(n \times 9 + 2\right) = \dfrac{16 + 72 \times n}{27 \times n + 6}
16,097
A^T*z*u = z*A^T*u
33,466
\frac{x^2}{x!} = \frac{1}{(x + \left(-1\right))!} + \frac{1}{(x + 2\cdot \left(-1\right))!}
14,409
a^l\cdot x = a^l\cdot x
27,613
2*\left(x + 1\right) = 2*x + 2
-19,072
1/2 = \frac{1}{49*\pi}*H_q*49*\pi = H_q
10,928
z^2 + z + 1 = (z + 2)\cdot \left(z + 2\right) = (z + (-1))\cdot (z + (-1))
17,914
2 \cdot (-1) + 2/3 \cdot q = 4 \cdot (q + 3 \cdot (-1))/6
39,838
\frac{n + 3}{n^2 + 3*(-1)} < \tfrac{n + 3}{n^2 + 9*(-1)} = \tfrac{n + 3}{(n + 3)*(n + 3*\left(-1\right))} = \frac{1}{n + 3*(-1)}
814
-z_1 * z_1*3 + z_1 z_2*10 - 3z_2^2 = (z_1 + z_2)^2 - (2z_1 - 2z_2)^2
31,778
17\times 16\times 15\times \dotsm\times 2 = 17!
49,984
\frac{1}{4} (k + 2)^4 = \frac14 (k + 1 + 1)^4 = \dfrac14 (k + 1)^4 + (k + 1)^2 + 1/4 + (k + 1)^3 + k + 1 + \frac12 (k + 1) (k + 1)
17,287
(-10 + 4\cdot \sqrt{10})/9 = -10/9 + \dfrac{\sqrt{10}\cdot 4}{9}
7,204
B^2 + (-1) = (B + 1)\cdot (B + (-1))
7,748
\frac1x \cdot 2 + 2 = \left(2 + x \cdot 2\right)/x
-182
\frac{1}{(8 + 4\cdot (-1))!}\cdot 8! = 8\cdot 7\cdot 6\cdot 5
21,644
(k\cdot 4 + \left(-1\right))^3 = 64 k^3 - 48 k^2 + k\cdot 12 + \left(-1\right)
18,225
1 = ((-1)^2)^{\dfrac12}
13,679
(4 + t^2 \cdot 4)^{1 / 2} = u \Rightarrow 4 \cdot t^2 + 4 = u \cdot u\wedge t^2 = \frac14 \cdot (u \cdot u + 4 \cdot \left(-1\right))
-26,576
2\times y^2 + 162\times (-1) = 2\times (y^2 + 81\times (-1)) = 2\times (y + 9)\times (y + 9\times (-1))
2,749
m = 5 \Rightarrow -1 = (-1)^m