id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-1,451 |
\tfrac{6\cdot 1/5}{(-1)\cdot 1/8} = \tfrac156 (-\frac81)
|
16,875 |
34 = 21*2 + 8*\left(-1\right)
|
15,363 |
(\alpha + \beta)*x = \beta*x + \alpha*x
|
33,487 |
-(-1) \cdot Z + I = I + Z
|
4,936 |
\mathbb{E}\left(\left(-1\right) + X\right) = \mathbb{E}\left(X\right) + \left(-1\right)
|
10,285 |
A^2\cdot B^3 = B \cdot B \cdot B\cdot A^2
|
37,059 |
|\dfrac{6}{n}|\cdot (2\cdot n + \left(-1\right)) = 10.5 \Rightarrow 4 = n
|
11,850 |
3^j\cdot 3 = 3^{j + 1}
|
27,487 |
[3,23] = 1 = [5, 23]
|
21,115 |
\sin(B + A) = \sin\left(A\right) \cos(B) + \sin\left(B\right) \cos(A)
|
5,993 |
(\sqrt{y} - \sqrt{y_0}) \cdot \left(\sqrt{y_0} + \sqrt{y}\right) = -y_0 + y
|
999 |
c_1/\left(c_2\right) = \frac{c_1}{c_2}\cdot 1^{-1} = c_1/(c_2) = c_1/(c_2)
|
-4,196 |
\frac{p}{p^5} = \frac{p}{p \cdot p \cdot p \cdot p \cdot p} = \frac{1}{p^4}
|
9,930 |
248 = 2 \times 2 \times 2 \times 31
|
26,022 |
\int 1/(\sqrt{y})\,\mathrm{d}y = \int y^{-\frac12}\,\mathrm{d}y
|
33,338 |
z g = g z
|
16,812 |
2 \cdot \cos{a} \cdot \sin{a} = \sin{a \cdot 2}
|
-6,423 |
\frac{1}{2\cdot (1 + t)}\cdot 2 = \dfrac{2}{2\cdot t + 2}
|
34,375 |
\frac{1}{3! \cdot 3! \cdot 3!} \cdot 9! = {9 \choose 3} \cdot {6 \choose 3} \cdot {3 \choose 3} = 1680
|
31,873 |
\cos(x) + \sin\left(x\right) = A\cdot \sin\left(x + x_0\right) = A\cdot \sin(x)\cdot \cos(x_0) + A\cdot \cos(x)\cdot \sin(x_0)
|
48,811 |
18 = \frac{36}{60}\times 30
|
27,846 |
2560 = 4^4 \cdot 10
|
7,161 |
2\times (1/2)^2 = 1/2
|
38,158 |
4^{-\frac13} = \frac{2^{\frac13}}{2}
|
-23,158 |
-8/9\cdot (-\frac23) = \frac{1}{27}\cdot 16
|
10,492 |
\omega = \frac{\omega}{5^{\frac13}}\cdot 5^{1/3}
|
14,251 |
144^{\sin^2\left(x\right)} = (12 \cdot 12)^{\sin^2(x)} = 12^{\sin^2(x)} \cdot 12^{\sin^2(x)}
|
-10,326 |
\frac{2*1/2}{15 k + 15 (-1)} = \frac{1}{k*30 + 30 (-1)}2
|
48,181 |
\frac{1}{\sqrt{x + (-1)}} + \dfrac{1}{\sqrt{(-1) + x}} \cdot \left(\left(-1\right) + x\right) = \frac{1}{\sqrt{\left(-1\right) + x}} + \sqrt{(-1) + x}
|
25,628 |
1 + 1 + 1 + 2 + 5 = 10
|
-23,955 |
9 + \tfrac{1}{5}45 = 9 + 9 = 9 + 9 = 18
|
-23,156 |
\frac{4}{3}*(-3/2) = -2
|
-3,398 |
10^{1/2} \cdot (5 + 4 + 2 \cdot (-1)) = 7 \cdot 10^{1/2}
|
5,148 |
n^2 - n*8 + 8 > 2n + 18 (-1) \Rightarrow 2n + 18 (-1) < n^2 - 8n + 8
|
-23,183 |
\tfrac{7}{2} = \frac{1}{2} \cdot 7
|
9,222 |
\frac{1}{c^2}*\left(b^2 - a^2\right) = \frac{1}{a^2}*(c^2 - b^2) = \dfrac{a^2 - c^2}{b * b}
|
-26,408 |
\frac{x^3}{x^4} = x^{-4 + 3} = \dfrac{1}{x}
|
7,741 |
((-1) + x)^2 + ((-1) + x)*2 = (-1) + x^2
|
5,438 |
\frac{1}{Z*H} = 1/(H*Z)
|
-20,878 |
\frac{1}{(-1) + y} \cdot (3 \cdot (-1) - y \cdot 10) \cdot \tfrac77 = \frac{1}{y \cdot 7 + 7 \cdot (-1)} \cdot (21 \cdot \left(-1\right) - 70 \cdot y)
|
-23,070 |
-7 \cdot -\dfrac{3}{2} = \dfrac{21}{2}
|
28,356 |
-(x + 2) \cdot 2 = 4 \cdot (-1) - x \cdot 2
|
14,110 |
2 + 2x = \frac{\mathrm{d}}{\mathrm{d}x} (x * x + x*2)
|
-22,317 |
V^2 - V*5 + 24*(-1) = \left(3 + V\right)*\left(8*(-1) + V\right)
|
-25,227 |
\frac{\text{d}}{\text{d}x} x^m = x^{m + (-1)} \cdot m
|
6,163 |
\frac{xy^2 + 4(-1)}{(-1) x^2 y} = -\frac{xy^2 + 4(-1)}{x^2 y} = \frac{1}{x^2 y}(-xy^2 + 4)
|
2,109 |
\left(7\cdot y^2 + 10\cdot y\cdot x + x^2\cdot 67\right)\cdot 7 = y^2\cdot 49 + x\cdot y\cdot 70 + 469\cdot x^2
|
-5,449 |
16.8/1000 = \frac{1}{1000}\cdot 16.8
|
19,026 |
a^4\cdot a^{30\cdot 67} = a^{2014}
|
20,487 |
|y + 3(-1)| = |y + \left(-1\right) + 2\left(-1\right)| \leq |y + \left(-1\right)| + 2
|
13,776 |
a^3+1=(a+1)(1-a+a^2)
|
5,310 |
1 + z^{2\cdot p} - 2\cdot z^p = (z^p + (-1))^2
|
-9,292 |
-x\cdot 2\cdot 5 - 2\cdot 2\cdot 3 = -10\cdot x + 12\cdot \left(-1\right)
|
23,081 |
5 + (29^{1 / 2} + 5\cdot (-1))/1 = 29^{\frac{1}{2}}
|
-1,138 |
5/6 \cdot (-\frac{8}{7}) = \frac{(-8) \cdot \frac17}{1/5 \cdot 6}
|
10,211 |
\left|{A + F^U}\right| = \left|{(A + F^U)^U}\right| = \left|{A^U + F}\right|
|
4,118 |
1/2 = 1/(\sqrt{2})\cdot \frac{1}{\sqrt{2}}\cdot 2/2
|
21,958 |
\frac{1}{b\cdot c} = 1/\left(b\cdot c\right)
|
9,647 |
\cos(35) = \cos(\frac{1}{3}*105)
|
23,361 |
1 + (4 + \left(-1\right))/2 = 1 + \frac32 = \frac22
|
16,312 |
m^2 \cdot 2^{\sqrt{m}} = \frac{1}{2^{-\sqrt{m}}} \cdot m^2
|
3,891 |
\frac{1}{q + (-1)}*q = \frac{1}{\left(-1\right) + q} + 1
|
10,321 |
\cot(i) = (\cos\left(i\cdot 2\right) + 1)/\sin(i\cdot 2)
|
-20,709 |
\frac{-54 \cdot q + 24}{20 \cdot \left(-1\right) + 45 \cdot q} = \frac{1}{q \cdot 9 + 4 \cdot \left(-1\right)} \cdot (9 \cdot q + 4 \cdot \left(-1\right)) \cdot \left(-\frac15 \cdot 6\right)
|
-22,837 |
\frac{5 \cdot 12}{6 \cdot 12} = 60/72
|
1,099 |
(-1) + m \cdot m = \left(m + 1\right) (m + (-1))
|
16,263 |
1 = \frac{1}{d_1} + \dfrac{1}{d_1 + d_2} + \frac{1}{d_1 + d_2 + f} \geq \frac{3}{d_1 + d_2 + f}
|
38,632 |
(2\cdot 6 + 3(-1))^{\dfrac{1}{2}} + 6 = 9 \neq 3
|
12,558 |
60 = 30\cdot x\Longrightarrow x = 2
|
7,314 |
\frac{(-1)^3}{3! \cdot 2^3} = -1/48
|
8,471 |
-\dfrac13 \cdot \left(X^2 - z^2\right)^{\frac{1}{2} \cdot 3} + C = C - (X^2 - z \cdot z) \cdot \sqrt{-z^2 + X^2}/3
|
-1,418 |
10/14 = \frac{5}{14*\frac{1}{2}}*1 = 5/7
|
2,108 |
d_2/(d_1) = \frac{1}{d_1\cdot \frac{1}{d_2}}
|
35,306 |
3^2 = 2 \cdot 2 \cdot 2 + 1^3
|
13,672 |
((6\cdot 2^{1 / 2}/2)^2 + (4\cdot 2^{1 / 2})^2)^{1 / 2} = 2^{\frac{1}{2}}\cdot 5
|
19,416 |
\sqrt{h \cdot h} = \sqrt{(-h)^2} = -h
|
-22,250 |
20 + r^2 - 9r = (r + 4(-1)) (5(-1) + r)
|
-1,296 |
\frac{1}{5}*7/2 = \frac{1}{2*\frac17 5}
|
13,074 |
\tfrac{3*\frac{1}{5}}{3}2*1/4 = 1/10
|
2,742 |
\left(\frac{b*h}{h}\right)^n = \frac{b^n*h}{h}*1
|
13,612 |
b^2 = a \cdot a \Rightarrow b = a
|
40,924 |
97 - 3588 + 36 \cdot 97 = 1
|
-16,515 |
6\cdot \sqrt{25\cdot 11} = \sqrt{275}\cdot 6
|
24,865 |
t^4 - t \cdot t + 2\cdot (-1) = (t^2 + 1)\cdot (t \cdot t + 2\cdot (-1))
|
22,075 |
1 + y^2 - 2 \cdot y = ((-1) + y)^2
|
-20,658 |
-7/3 \cdot \frac{1}{p + 10 \cdot (-1)} \cdot (10 \cdot (-1) + p) = \dfrac{-7 \cdot p + 70}{30 \cdot \left(-1\right) + 3 \cdot p}
|
2,758 |
2x\pi = 2\pi r_2 \implies x = r_2
|
33,112 |
\frac{1}{2} \cdot \left(11 + (-1)\right) = 5
|
9 |
2*\cos^2{s*x} + (-1) = \cos{2*x*s}
|
-4,426 |
\frac{1 - z\cdot 3}{z^2 - z\cdot 2 + 3\cdot (-1)} = -\frac{1}{z + 3\cdot (-1)}\cdot 2 - \frac{1}{z + 1}
|
31,126 |
{7 \choose 2} = 7\cdot 6/2 = 21
|
-11,706 |
16^{-\frac12} = (\frac{1}{16})^{\frac{1}{2}} = \dfrac14
|
11,491 |
1 + 1 + 1 + \dotsm = -\frac12
|
-1,114 |
-\frac71 \cdot (-\frac{2}{3}) = \frac{\frac13 \cdot (-2)}{1/7 \cdot (-1)}
|
-2,272 |
\dfrac{7}{15} - 1/15 = \dfrac{6}{15}
|
8,153 |
\tan^2{c \cdot z} = \tan^2{-c \cdot z}
|
-4,242 |
\tfrac{y\times 3}{2} = y\times 3/2
|
18,023 |
\int\limits_{t_0}^t 1\,dt = \int_0^s 1\,ds \implies t = t_0 + s
|
-7,408 |
\dfrac16 = 4/9\cdot \frac18\cdot 3
|
17,935 |
5 = 25 + 20 \times (-1)
|
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