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ddrg
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math_formulas

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-4,433
\frac{-x + 5}{x^2 + x\cdot 8 + 15} = \frac{4}{x + 3} - \frac{5}{x + 5}
5,504
\tfrac{4*I + 3}{7*I + 5*\left(-1\right)} = \frac{1}{-5/I + 7}*\left(4 + \frac3I\right)
759
{n \choose j} \cdot j = \frac{1}{(j + (-1))! \cdot (n - j)!} \cdot n! = n \cdot {n + (-1) \choose j + (-1)}
4,970
z \cdot z\cdot 2 + 5\cdot z\cdot y + 2\cdot y \cdot y = (2\cdot z + y)\cdot (z + 2\cdot y)
13,018
2*x * x - x + 3*(-1) = \left(x + 1\right)*2*(x + 3*(-1)) = 2*(x + 1)*(x + 3*\left(-1\right))
44,453
1 + 3 \times 5 = 16
-15,036
\tfrac{1}{\frac{h^5}{t^{20}}\times t^4} = \tfrac{1}{t^4\times \frac{1}{t^{20}\times \frac{1}{h^5}}}
22,679
\frac{1}{6}\cdot 10 + \frac16\cdot 9 + 4/6\cdot 7 = \dfrac{47}{6} < 8
7,982
(1 + 5^{1 / 2})/2 = 1/2 + \frac{5^{\frac{1}{2}}}{2}
19,339
2*\frac{1}{6}/2 = \frac16
22,397
\frac13 + 2/3\cdot (\dfrac{2}{3}\cdot 2 + \frac{1}{3}\cdot 3) = 17/9
34,085
2 (-1) + 2 \cdot 2 + 1 = 3
15,102
(w * w * w)^3 = w^9
22,163
0 = 3 + 6 \cdot z \Rightarrow z = -1/2
-1,135
\dfrac{56}{24} = 56\cdot 1/8/(24\cdot 1/8) = 7/3
31,403
-10 + 2\cdot 6 = 2
522
5 - 0 \cdot 3 + 9/3 = 5 + 0\left(-1\right) + 9/3 = 5 + 0(-1) + 3 = 5 + 3 = 8
-24,681
-30\cdot i + 52\cdot (-30\cdot i) = -30\cdot i + 52\cdot (-30\cdot i) = 52\cdot \left(-30\cdot i\cdot (-30\cdot i)\right) = 52\cdot (-60\cdot i)
-8,063
\dfrac12 \cdot (7 + i - 7 \cdot i + 1) = \frac{1}{2} \cdot (8 - 6 \cdot i) = 4 - 3 \cdot i
22,403
|2 \left(-1\right) + z| |z + (-1)| = |z^2 - 3 z + 2|
23,995
\int_f^b k\,\mathrm{d}z = \int\limits_f^b k\,\mathrm{d}z
22,446
c^2\cdot d^2 = (c\cdot d)^2
-7,077
\frac{3}{13} \cdot 4/14 = 6/91
25,978
(-1)^n\cdot {-2 \choose n} = {n + 1 \choose n} = {n + 1 \choose 1} = n + 1
-1,119
-\dfrac16\times 5/6 = (\left(-1\right)\times 1/6)/(6\times 1/5)
11,226
(x + y)^2 = x^2 + y\cdot x\cdot 2 + y \cdot y
-22,701
5\cdot 11/(9\cdot 11) = \dfrac{1}{99}55
28,673
17296 = \frac{103776}{3 \cdot 2} 1
-3,147
13^{1/2} \cdot \left(1 + 3\right) = 13^{1/2} \cdot 4
-2,330
2/15 = 3/15 - 1/15
15,030
7/33 = \dfrac{105}{495}
20,244
-2\cdot \sin^2{c} + 1 = \cos{c\cdot 2}
4,854
\frac{2}{1 + l} = \frac{l!}{2^l} \tfrac{2^{l + 1}}{\left(l + 1\right)!}
23,532
2 + 2*(m + (-1)) = 2*m
35,995
2 \cdot \left(y^2 + y\right) \cdot \left(y^2 + y\right) - 2 \cdot y^4 - y^2 \cdot 2 = 4 \cdot y^3
23,721
64\cdot t^2 + 16\cdot t + 1 = (\frac{1}{8} + t)^2\cdot 64
-23,245
\dfrac{3}{7} \cdot \dfrac{4}{9} = \dfrac{4}{21}
-12,223
2/5 = \dfrac{1}{6 \cdot \pi} \cdot s \cdot 6 \cdot \pi = s
29,506
\left(1 + n\right) ((-1) + n) n = -n + n^3
3,388
s + E = E + D = 0, D + s = 1 \Rightarrow -E = D = s = \frac12
25,736
\frac{1}{x^9 \cdot z^9} \cdot (x^9 + z^9) = \frac{1}{x^9} + \frac{1}{z^9}
31,135
0.5999999*\ldots = 5.4/9 = 0.6
13,350
1 - 126/495 = 1 - 42/165 = \frac{1}{165}\cdot 123 = 0.7454545\cdot \dotsm
-6,694
\frac{3}{10} + \dfrac{9}{100} = \frac{1}{100}9 + 30/100
6,903
\frac{n + n^2}{n^2 + 1} = 1 + \frac{n + (-1)}{n * n + 1}
35,618
d\cdot x + b\cdot y = x\cdot d + b\cdot y
1,360
\frac{r}{2}\cdot h\cdot 2 = h\cdot r
34,028
t^2 + (-1) = (t + (-1)) (1 + t)
16,262
z\cdot s = a \Rightarrow \bar{a} = s\cdot \bar{z}
-13,922
\frac{42}{8 + 6} = \dfrac{1}{14}\cdot 42 = 42/14 = 3
7,637
n_2\times n_1\times \tfrac{1}{n_2}/(n_1) = 1/(n_2)\times n_1\times n_2/(n_1)
26,547
\sin(x) = \sin^2(x)/\sin(x) = \sin\left(x\right)
856
d^6 = h d^4 h \Rightarrow d^4 = h d^6 h = d^9
40,662
\frac{5}{8} = \frac58
22,410
\dfrac{\cos{x}}{-1} - \int 0/1 \times \cos{x}\,\mathrm{d}x = \int \sin{x}\,\mathrm{d}x
-1,591
\tfrac13 \cdot 4 \cdot \pi = \pi \cdot 2 - \pi \cdot 2/3
9,401
f_2^2\cdot f_1^2 + \left(-1\right) = \left(1 + f_2\cdot f_1\right)\cdot ((-1) + f_2\cdot f_1)
32,541
5/8 = 1/2 + \frac14 - \frac18
13,234
\frac{8}{3\cdot 2}\cdot 9\cdot 10 = 120
5,427
\left(x + 1\right)! + (x + 1)! \cdot (x + 1) = \left(x + 1\right)! \cdot (1 + x + 1) = \left(x + 2\right)!
9,680
\frac{1}{17^2} \cdot 48^2 \cdot \left(34^2 - x^2\right) = (95 - x) \cdot (95 - x) = 95^2 - 190 \cdot x + x^2
-20,663
\frac{8}{3} \cdot 6/6 = 48/18
-20,453
(-n \cdot 70 + 56 \cdot (-1))/\left(-70\right) = \frac{7}{7} \cdot (-10 \cdot n + 8 \cdot (-1))/(-10)
14,307
-\lambda = \frac{T'}{T} \Rightarrow T\lambda + T' = 0
-23,046
-\dfrac52 = 5(-1/2)
25,044
\frac{z \cdot z}{-z + z^2} + \frac{1}{-z + z^2} = \frac{1 + z^2}{z^2 - z}
-25,130
\frac{\omega \cdot 36 + \omega \cdot \omega \cdot 75}{2 \cdot \sqrt{5 \cdot \omega + 3}} = \frac{d}{d\omega} (3 \cdot \sqrt{3 + 5 \cdot \omega} \cdot \omega^2)
1,443
\frac1d \cdot \left(c + d\right) = \frac{c}{d} + 1
31,556
0.234375 = 1 - 7/8*\frac{7}{8}
-10,540
-\frac{1}{16*t^3}*20 = -\dfrac{1}{t^3*4}*5*\frac14*4
25,437
G*2890 = G*289*10
31,193
g \cdot g - c^2 = (-c + g) \cdot (c + g)
21,389
2*5^2 - 8*5 + 9(-1) = 1
13,181
y^{\frac{1}{2}}/y = y^{\dfrac{1}{2} + (-1)} = y^{-1/2} = \frac{1}{y^{1/2}}
98
\tfrac{1}{z/2 + 1}*(1 + \left(-1\right) - z/2) = -1^{-1} + \frac{1}{1 + \frac{z}{2}}
1,239
\frac{1}{100}\cdot 19 = 1/100 + \frac{9}{100} + 9/100
8,592
{6 \choose 2}\cdot 4! = 6!/2!
22,640
\cos(|z\times y|) = \cos{-z\times y} = \cos{z\times y}
-12,175
\dfrac{9}{20} = \dfrac{q}{12 \cdot \pi} \cdot 12 \cdot \pi = q
26,217
80\cdot 800 = 800/1\cdot \frac{800}{10}
-11,737
(\frac{1}{2})^2 = \frac{1}{4}
8,929
\frac{1}{B*Y} = \frac{1}{B*Y}
-22,219
a^2 - a + 30 \cdot (-1) = (6 \cdot (-1) + a) \cdot (5 + a)
10,276
\frac{1}{cac^2 \cdot \frac{1}{a^2 c^6}} = c^6 a^2 \frac{1/c}{c^2}\tfrac1a
19,899
HH A = HHA
40,115
3! = \frac{4!}{4}
11,221
\left|{x*M}\right| = \left|{x*M}\right|
28,667
x = k + (-1) \implies x + 1 = k
17,433
\omega^x + \omega^x*(a_x + \left(-1\right)) = a_x*\omega^x
19,129
\sin(\cos{y})*3 \sin{y} = 3\sin(\cos{y}) \sin{y}
21,438
\dfrac{13}{4} \cdot 1/51 = \frac{1}{204} \cdot 13
502
G\cdot 4 = 1 \implies \frac{1}{4} = G
15,499
\left(-1\right) + c^n = (\left(-1\right) + c) \cdot (c^{\left(-1\right) + n} + c^{2 \cdot (-1) + n} + \dotsm + c + 1)
364
(r + 2 \cdot r) \cdot \cot(\pi/4) = r \cdot 3
-5,205
10^1*58.8 = 10^{2 - 1}*58.8
-7,465
\tfrac92 = 27/6
12,189
(-5)^2 + (-3)^2 + 1 * 1 = 35 = 5*((-5)*(-3) - 5 - 3)
51,819
12 \cdot 13 \cdot 14 \cdot 15 = 32760
24,517
0 + x + 0 \cdot \dots = x
-14,116
\tfrac{18}{6 + 4 \cdot (-1)} = 18/2 = 18/2 = 9