id
int64
-30,985
55.9k
text
stringlengths
5
437k
-20,138
-\frac49 \cdot \frac{1}{y \cdot 9 + 3 \cdot (-1)} \cdot (y \cdot 9 + 3 \cdot (-1)) = \frac{-y \cdot 36 + 12}{27 \cdot (-1) + y \cdot 81}
-4,440
\dfrac{5}{4*\left(-1\right) + x} + \frac{4}{2 + x} = \frac{1}{8*(-1) + x^2 - 2*x}*(x*9 + 6*(-1))
15,951
1 - \frac{1}{k^2} = \tfrac{1}{k^2} \cdot (k + \left(-1\right)) \cdot (1 + k)
-12,063
14/15 = x/(16\cdot \pi)\cdot 16\cdot \pi = x
2,123
D \cdot b \cdot c = b \cdot D \cdot c
9,215
1 + \frac{1}{l^2} - \frac{1}{l} \cdot 2 = (-\frac{1}{l} + 1)^2
30,416
134 = 11^2 + 3 \cdot 3 + 2^2 = 10^2 + 5 \cdot 5 + 3^2 = 9^2 + 7^2 + 2^2 = 7^2 + 7 \cdot 7 + 6^2
28,979
\left(a - b\right)\cdot (b + a) = a^2 - b \cdot b
15,929
\binom{6}{2}*4! = \frac{6!}{2!*4!}*4! = 6!/2! = 360
-3,335
\sqrt{3}\cdot (3 + 1) = 4 \sqrt{3}
9,002
\frac{1}{7}\times (12 + 144 + 20 + 3\times \sqrt{4}) + 5\times 11 = 9 \times 9 + 0
22,125
\cos{2\cdot u} = 2\cdot \cos^2{u} + (-1)
13,646
y^{\frac{1}{2}}/y = y^{\frac{1}{2} + (-1)} = y^{-\frac12} = \frac{1}{y^{\frac{1}{2}}}
24,016
x_4 - 4\times x_3 + x_2\times 6 - x_1\times 4 + x_0 = x_4 - 3\times x_3 + 3\times x_2 - x_1 - -x_0 + x_3 - x_2\times 3 + x_1\times 3
41,480
S_z = S_z
6,265
0 = q^2 + q + 15 \cdot (-1)\Longrightarrow (-1 \pm \sqrt{61})/2 = q
10,288
\binom{14}{2} = 91 = \tfrac{182}{2} \cdot 1
929
y^2 + y\cdot g\Longrightarrow \left(y + g/2\right)^2 - (\frac{g}{2})^2
917
x*(v + w) = x*v + w*x
8,172
\dfrac{1}{I - x} = \frac{1}{I - x}\times (I - x + x) = I + \frac{x}{I - x}
34,950
4 = 2! \cdot 2
27,004
F*x = F*x
14,747
\frac{117.7}{0.07 + 1}\cdot \frac{1}{1 + 0.1} = 100
2,902
x \cdot x^2 + y^3 = (x^2 - x \cdot y + y^2) \cdot (x + y)
11,055
(x^{2 \cdot c})^f = ((x^c)^2)^f = (\frac{1}{x^c})^f = \left(x^c\right)^{f + (-1)}
34,851
y = k = 15 rightarrow y - k
13,737
9\cdot y^2 + 36\cdot \left(-1\right) = 3\cdot y^2 - 6^2 = (3\cdot y + 6)\cdot (3\cdot y + 6\cdot (-1)) = 3\cdot (y + 2)\cdot \left(3\cdot y + 6\cdot (-1)\right) = 9\cdot (y + 2)\cdot \left(y + 2\cdot (-1)\right)
-26,160
5 \cdot \sin(-\frac12 \cdot 5 \cdot \pi) - 5 \cdot \sin(-2 \cdot \pi) = -5 + 0 \cdot (-1) = -5
11,667
-4*(-1) + 1 * 1 = 5
30,980
\frac{1}{4} \cdot \pi + \pi/6 = \pi \cdot 5/12
2,782
(x + y) * (x + y) = x^2 + y^2 + 2yx
24,973
l = 2^j \implies j = \log_2(l)
28,771
29 + (x + 3*\left(-1\right))^2 = 38 + x^2 - x*6
-11,762
(1/16)^{\frac14} = 16^{-\dfrac{1}{4}}
7,595
r^n\cdot b = z\cdot r\cdot h \Rightarrow h\cdot z = r^{(-1) + n}\cdot b
-29,572
\frac1y\cdot (3\cdot y^2 + 10\cdot (-1)) = 3\cdot y^2/y - 10/y
-22,255
6*\left(-1\right) + k^2 + k*5 = (k + 6)*\left(k + (-1)\right)
-19,180
25/36 = \frac{Y_t}{81 \times π} \times 81 \times π = Y_t
16,945
v = x^3 \Rightarrow x^2\cdot 3 = \frac{dv}{dx}
10,951
\binom{1 + p}{2} + \binom{(-1) + r}{2} - \binom{p}{2} - \binom{r}{2} = 1 + p - r
-5,885
\frac{l}{(l + 2\cdot (-1))\cdot (6\cdot (-1) + l)} = \tfrac{1}{l^2 - 8\cdot l + 12}\cdot l
-22,240
(7 + r)*\left(6*\left(-1\right) + r\right) = r^2 + r + 42*(-1)
-7,193
\dfrac29 = \frac{2}{5} \cdot \frac59
-20,687
\frac{1}{-y \cdot 14 + 70} \cdot (y \cdot (-35)) = \dfrac{1}{-y \cdot 2 + 10} \cdot (y \cdot \left(-5\right)) \cdot 7/7
-22,908
40/24 = 5\cdot 8/(8\cdot 3)
-4,701
\frac{16*\left(-1\right) - 6*x}{6 + x^2 + x*5} = -\frac{4}{2 + x} - \tfrac{2}{x + 3}
14,781
680 = 17^1*2 * 2 * 2*5^1
23,132
10^{2k + 1} + 10^{2k + 1} + \left(-1\right) = 2 \cdot 10^{2k + 1} + (-1) = 20 \cdot 10^{2k} + \left(-1\right)
47,106
119 = 17\times 7
20,913
b^m\cdot a^m = b^m\cdot a^m
-11,706
16^{-1/2} = (\dfrac{1}{16})^{\frac12} = 1/4
19,348
43 = 3 \cdot (21 - x) - x = 63 - 4x
29,868
\dfrac{1}{2z^3 + \sqrt{z^6}}\left(9z * z * z + 5\right) = \frac{1}{3z^3}(9z^3 + 5) = 3 + \frac{5}{3z^3}
-13,330
\frac{1}{8 + 7}*90 = \frac{1}{15}*90 = \frac{90}{15} = 6
-8,355
-30 = 6(-5)
23,980
\tfrac{\pi*3}{4} = -\frac{\pi}{4} + \pi
15,090
\left(-\frac{1}{2}\right)^{-\dfrac12} = (-\tfrac12)^{-\frac14\cdot 2} = (\dfrac{1}{\frac{1}{4}})^{-1/4} = 4^{-\frac{1}{4}} = 1
-18,763
(-1) \times 0.003 + 0.0228 = 0.0198
3,543
y^2 - y + 2 \cdot (-1) = \left(y + 2 \cdot (-1)\right) \cdot (y + 1)
13,246
0 = (c_1 + c_2)\times 10 + \frac1e\times c_1 \Rightarrow c_2 = -c_1/\left(10\times e\right) - c_1
-3,992
k * k/k = \frac{k}{k}*k = k
24,113
5/4 - \frac65 = \frac{1}{20}
35,738
\left(m + 1\right)^5 - m + 1 = m^5 + 5 \cdot k + 1 - m + 1 = 5 \cdot k + m^5 - m
12,690
a = x*3 \Rightarrow a^2 = 9x * x = 3*3x^2
-28,983
4 \cdot \pi/6 = \pi \cdot 2/3
26,535
\frac{1}{\sqrt{-x^2 + 1}} = \frac{\mathrm{d}}{\mathrm{d}x} \arcsin(x)
38,652
1 + \pi = 2 + \pi + \left(-1\right)
25,383
( E\times Y, F\times Y) = (F\times Y)^x\times E\times Y = Y^x\times F^x\times E\times Y = Y^x\times F^x\times E\times Y
2,987
y/2 = 2 \cdot \sqrt{y} \cdot \frac22 \cdot \sqrt{y} \cdot \dfrac{1}{4}
21,651
1/x = g \cdot \frac{x}{g} = g \cdot g \cdot \frac{1}{x \cdot g^2}
27,349
(f + \left(-1\right))^1 = f^1 + (-1)^1
20,693
v \cdot a = f_1 \cdot f_2 \implies v = f_2 \cdot f_1/a
-18,619
-26/12 = -\frac{13}{6}
14,873
\binom{8}{3} + 4 \binom{8}{4} + \binom{8}{5} \cdot 5 + \binom{8}{6} = 644
-19,459
6/1 \cdot \frac{5}{3} = 5 \cdot \frac{1}{3}/\left(\tfrac{1}{6}\right)
14,651
\frac{z^{m + 1}}{m\cdot z^m}\cdot (m + 1) = (m + 1)\cdot z/m = (1 + 1/m)\cdot z
20,554
z*F + G*z = m \Rightarrow (F + G)*z = m
3,201
w \cdot w^2 = -2w + (-1) = w + 2
24,848
\frac{1}{x^2 + 2}\cdot x^3 = \dfrac{x^3\cdot \tfrac12}{1 + x^2/2}
22,182
-Z*F + Z*F = F \Rightarrow Z*F^2 - F*Z*F = F^2
5,278
q\cdot 2 + \left(-1\right) = q + 4 \Rightarrow q = 5
28,591
\dfrac{1}{\frac{1}{a - \frac1b} - \frac{1}{a}} = a \cdot b \cdot a - a
19,121
z^2 - (\pi + e)\cdot z + \pi\cdot e = (z - e)\cdot \left(-\pi + z\right)
25,767
-\dfrac16 + \dfrac{1}{2} + 1 = 4/3
-29,239
20 = 5\cdot 4 + 0\cdot (-1)
-2,115
\frac{7}{6}*\pi + \pi*\frac76 = \pi*\frac{1}{3}*7
1,513
\sin{x\times 2} = \cos^2{t} \Rightarrow \sin{2\times x} + 1 = (\cos{x} + \sin{x})^2 = \cos^2{t} + 1
13,218
e^A*A = A*e^A
15,967
\left(7\cdot \left(-1\right) + 9\right)\cdot (9 + 3) = 24
53,762
\tfrac{3 / 8}{\dfrac{1}{2 \cdot 4} + \dfrac{3 / 4}{2} \cdot 1} \cdot 1 = 3/4
10,987
-(\frac12)^2 + 3/10 = \frac{1}{20}
-13,823
\dfrac{36}{1 + 5} = 36/6 = \frac{36}{6} = 6
-30,261
\frac{1}{x + 3}*(x^2 - x + 12*(-1)) = \frac{(x + 4*(-1))*(x + 3)}{x + 3} = x + 4*(-1)
25,648
\cos(a)\cdot \cos\left(b\right) - \sin(b)\cdot \sin(a) = \cos\left(b + a\right)
12,087
-b + r \lt 0 \implies r < b
21,276
0 = 1/y \implies y\cdot 0 = 1
20,006
h \cdot (b + e) = e \cdot h + h \cdot b
4,807
x^2 + 4xz + z^2 = -(z + x*4)^2*3 + (x*7 + 2z)^2
3,744
-3h + g*7 = 6g - h*3 + g
-20,931
\tfrac{7}{7} \cdot \frac{1}{4 \cdot (-1) + x} \cdot (x + (-1)) = \frac{7 \cdot (-1) + 7 \cdot x}{28 \cdot (-1) + 7 \cdot x}