id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
9,392 |
y^2 = y^2 - 4y + 4 + 4y + 4(-1) = (y + 2(-1))^2 + 4y + 4(-1)
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1,033 |
\frac12*((-1) + 1 + k*2) = k
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30,635 |
85/2 = \frac16\cdot 255
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-1,129 |
8/1\cdot (-\frac12) = \dfrac{1}{1/8}\cdot \left(\left(-1\right)\cdot 1/2\right)
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-24,118 |
\left(1 + 9\right)^2 = 10 \cdot 10 = 10^2 = 100
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20,499 |
0 \gt \sin(\alpha)\Longrightarrow \alpha = -\tfrac{\pi\cdot 2}{3}\cdot 1
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55,859 |
1 = 0^0
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37,092 |
\dfrac{1}{x^2 + 4\cdot \left(-1\right)}\cdot (x + 2\cdot (-1)) = \frac{x + 2\cdot (-1)}{\left(x + 2\cdot (-1)\right)\cdot \left(x + 2\right)} = \frac{1}{x + 2}
|
-24,650 |
-\frac{1}{10}\cdot 3 + 1/4 + 3/5 = 11/20
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-1,282 |
\left((-1)*1/3\right)/(7*1/8) = 8/7 (-\dfrac13)
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-5,117 |
\dfrac{0.82}{100} = \frac{1}{100} \cdot 0.82
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37,628 |
|(-1) (-1) + x| = |x + 1|
|
13,670 |
|1/(z_1) - \frac{1}{z_2}| = |(-z_2 + z_1)/(z_2\cdot z_1)|
|
31,928 |
2*(1 + 2 + \dots*n) = (n + 1)*n
|
33,370 |
24 = 2^2\cdot {4 \choose 2}
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8,968 |
-\frac{1}{2} \cdot \cos(2 \cdot \theta) + 1/2 = \sin^2(\theta)
|
8,875 |
\cos(x + z) = -\sin{z} \sin{x} + \cos{z} \cos{x}
|
12,487 |
\tan^{-1}(\infty)*4 = \pi*2
|
7,636 |
(n + 1)^2 = 1 + 3 + 5 + \dotsm + n\cdot 2 + 1
|
-20,715 |
\frac{1}{24 \cdot k} \cdot (6 + 27 \cdot k) = 3/3 \cdot \frac{1}{k \cdot 8} \cdot (k \cdot 9 + 2)
|
-1,819 |
19/6 \pi - \pi\cdot 2 = \pi \frac76
|
19,511 |
\frac{50}{2} \cdot \frac{1}{100} = \frac{1}{2 \cdot 2} = \tfrac14
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-26,401 |
z^k z^m = z^{m + k}
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-23,125 |
-1/2*5/8 = -5/16
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-9,137 |
-p^2\times 42 - p\times 63 = -p\times 2\times 3\times 7\times p - p\times 3\times 3\times 7
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-20,576 |
-\frac85*\frac{2*x + 2*(-1)}{2*x + 2*(-1)} = \frac{-16*x + 16}{10*(-1) + x*10}
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22,067 |
\frac{\Delta*z_2}{\Delta*z_1} = \frac{z_2*\Delta}{z_1*\Delta}
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-2,155 |
π/2 + π*\frac16*11 = 7/3*π
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-20,553 |
\frac{1}{z \times 80} \times ((-56) \times z) = -\frac{1}{10} \times 7 \times \dfrac{z \times 8}{z \times 8} \times 1
|
9,877 |
\dfrac{1}{15} = \dfrac{1/20}{3 \cdot 1/4}
|
2,952 |
\frac{2 x y}{x + y} = \dfrac{2}{\frac{1}{x} + \frac1y} \leq \tfrac12 (x + y)
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27,614 |
(1 + 0.5 + 0.5^2)\cdot 305 = 305 + (1 + 0.5)\cdot 305\cdot 0.5
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24,959 |
\frac34 = \frac{1}{2} \cdot \tfrac{3}{2}
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-7,619 |
10/5 - \dfrac{i*10}{5} = (10 - i*10)/5
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-14,545 |
4*(6 + 3) = 4*9 = 36
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7,007 |
c = h \cdot l,b = h \cdot n\Longrightarrow \left(l \pm n\right) \cdot h = c \pm b
|
44,540 |
π = \frac{π}{2} + \dfrac{π}{2}
|
-20,917 |
\dfrac{48 \cdot x + 64}{x \cdot 18 + 24} = 8/3 \cdot \frac{1}{8 + 6 \cdot x} \cdot (x \cdot 6 + 8)
|
23 |
\|\frac{1}{\frac1A}\|*\|\frac1A\| = \|\frac1A\|*\|A\|
|
28,699 |
(x + 1) (4(-1) + x) = 4(-1) + x^2 - x*3
|
-19,071 |
\frac{1}{3}2 = \frac{Y_x}{64 \pi} \cdot 64 \pi = Y_x
|
8,951 |
\left(\left(I = o \cdot A \Rightarrow A \cdot o \cdot A = I \cdot A = A\right) \Rightarrow \frac{A}{A} = \frac1A \cdot o \cdot A^2\right) \Rightarrow I = A \cdot o
|
5,821 |
0 = -25 \cdot \frac{55}{25} + 80 + 25 \cdot (-1)
|
-2,984 |
\sqrt{7} \sqrt{9} + \sqrt{25} \sqrt{7} = 5 \sqrt{7} + \sqrt{7} \cdot 3
|
-23,720 |
\tfrac{3}{7} \cdot 4/5 = 12/35
|
36,904 |
x^{91} = \left(x^7\right)^{13}
|
43,239 |
5 \cdot 8 \cdot 8 = 320
|
29,345 |
4^2 + 3^2 = 0^2 + 5^2
|
-20,719 |
\frac{1}{30 \cdot \left(-1\right) + z \cdot 10} \cdot (-z \cdot 9 + 27) = \dfrac{1}{z + 3 \cdot (-1)} \cdot (3 \cdot \left(-1\right) + z) \cdot (-\dfrac{9}{10})
|
51,863 |
\sum_{m=1}^\infty (\frac12 + (-1)^m)/m = \sum_{m=1}^\infty \tfrac{1}{2 \times m} + \sum_{m=1}^\infty (-1)^m/m = \left(\sum_{m=1}^\infty 1/m\right)/2 + \sum_{m=1}^\infty \frac1m \times (-1)^m
|
2,456 |
k + (-1) + y^l = (k + (-1))*\left(y^{l + \left(-1\right)} + \dotsm + y + 1\right)
|
18,064 |
1 + z^2 + z*2 = z^2 + 3(-1) + 2z + 4
|
3,007 |
\left((a + f)^2 - 4\cdot a\cdot f\right)^{1/2} = ((a - f) \cdot (a - f))^{1/2} = |a - f|
|
-20,680 |
\frac{1}{-8 \cdot \varphi + 2 \cdot (-1)} \cdot (-\varphi \cdot 3 + 7 \cdot (-1)) \cdot 3/3 = \frac{1}{-24 \cdot \varphi + 6 \cdot (-1)} \cdot (-9 \cdot \varphi + 21 \cdot (-1))
|
30,946 |
\dfrac{x_0}{x_1} = \dfrac{1}{x_1}x_0
|
6,059 |
\tfrac{1}{3 + 2\cdot k}\cdot (\left(-1\right) + k\cdot 2) = -\frac{4}{2\cdot k + 3} + 1
|
-23,449 |
\dfrac{1}{21} \cdot 10 = 2/3 \cdot \frac{1}{7} \cdot 5
|
3,929 |
2 + 6*k = 3*2*k + 2
|
-15,825 |
0 = 5*5/10 - 5/10*5
|
-26,629 |
(4 \cdot z)^2 - (7 \cdot y)^2 = (z \cdot 4 - y \cdot 7) \cdot (4 \cdot z + 7 \cdot y)
|
26,153 |
1 - y/c = \frac{1}{c}\times (-y + c)
|
-20,997 |
\dfrac{1}{r \cdot 8}(-r \cdot 4 + 12 (-1)) = \tfrac{1}{2r}(3\left(-1\right) - r) \cdot 4/4
|
51,005 |
e/2 - e^2/4 + \frac{e^3}{6} - \dots = \sum_{\omega=1}^\infty (-1)^{\omega + (-1)}\cdot e^\omega/(2\cdot \omega) = \sum_{\omega=0}^\infty (-1)^\omega\cdot \frac{e^{\omega + 1}}{2\cdot (\omega + 1)}
|
9,846 |
z - -f = z + f
|
12,047 |
2 2 (2 + 1)^2/4 = 36/4 = 9
|
24,547 |
2 + 12\cdot k = k\cdot 5 + 1 + k\cdot 7 + 1
|
17,819 |
3 - 2\cdot g = g + d + e - 2\cdot g = -g + d + e
|
14,858 |
\dfrac{1}{dx^2} \cdot dy^2 = (\frac{1}{dx} \cdot dy)^2
|
-19,998 |
\frac{9}{1} \frac{3 - 9n}{3 - 9n} = \frac{-n\cdot 81 + 27}{3 - n\cdot 9}
|
-17,681 |
64*\left(-1\right) + 89 = 25
|
1,302 |
\sin(s\cdot 2) = \cos\left(s\right)\cdot \sin(s)\cdot 2
|
13,074 |
\frac{2/4\cdot \frac{3}{5}}{3} = \frac{1}{10}
|
-27,383 |
379\times (-1) + 960 = 581
|
11,244 |
\tfrac{1}{4} + (-1) = -\frac34
|
-2,156 |
\dfrac{\pi}{6} - 5/3\cdot \pi = -\pi\cdot 3/2
|
27,946 |
\cot(z) - \tan(z) = \frac{\cos(2\cdot z)}{\sin\left(2\cdot z\right)}\cdot 2 = 2\cdot \cot\left(2\cdot z\right)
|
-20,383 |
-4/9 \times \frac{1}{9 \times (-1) + x} \times (x + 9 \times (-1)) = \dfrac{36 - 4 \times x}{9 \times x + 81 \times (-1)}
|
11,279 |
d/dy \sin(y) = 2\cdot \cos(y)\cdot \pi
|
29,556 |
((-1)\cdot \pi)/2 = -\frac{1}{2}\cdot \pi
|
44,697 |
21*7 = 147
|
-5,468 |
\frac{1}{20 (-1) + 4 x} = \frac{1}{4 (5 \left(-1\right) + x)}
|
3,065 |
2 - \frac{2}{3 - x} = \frac{1}{3 - x}\cdot (4 - 2\cdot x) = \frac{1}{3 - x}\cdot 2\cdot (2 - x)
|
17,979 |
\frac{1 - \frac{D}{-d + f}}{\tfrac{D}{f - d} + 1} = \frac{f - d - D}{f - d + D}
|
26,417 |
f_1^2 - f_2 f_1 + f_2^2 = (f_1 - f_2)^2 + f_1 f_2
|
19,453 |
\cos(\theta) - i\cdot \sin(\theta) = \cos\left(-\theta\right) + \sin(-\theta)\cdot i
|
-713 |
({ e^{5\pi i / 3}}) ^ {15} = e ^ {15 \cdot (5\pi i / 3)}
|
-12,056 |
\frac{9}{10} = \frac{t}{20 \cdot \pi} \cdot 20 \cdot \pi = t
|
33,171 |
2*2 = 2 * 2
|
15,718 |
\frac{5!}{2!*2!} = \frac14*120 = 30
|
32,541 |
-1/8 + 1/2 + \frac{1}{4} = \dfrac{1}{8}\cdot 5
|
18,357 |
73 = \left(19 - 2^{1/2}\cdot 12\right)\cdot (19 + 2^{1/2}\cdot 12)
|
-9,454 |
-15 \cdot n + 35 \cdot (-1) = -7 \cdot 5 - n \cdot 3 \cdot 5
|
-19,890 |
0.01 (-93) = -\frac{93}{100} = -0.93
|
28,335 |
\sqrt{a^2 \cdot \sinh^2{p} + a^2} = a \cdot \sqrt{\sinh^2{p} + 1} = a \cdot \cosh{p}
|
571 |
\binom{2^n}{2} + (-1) = \frac{1}{2}\cdot 2^n\cdot (2^n + (-1)) + (-1) = \frac12\cdot (2^{2\cdot n} - 2^n + 2\cdot (-1))
|
7,012 |
1/(u\frac{x}{u}) = u\frac{1}{ux}
|
10,355 |
h^2 = (k + 3 (-1)) (k + 3 (-1)) + (h + 4 (-1))^2 \implies (k + 3 (-1))^2 = h h - (h + 4 (-1))^2 = 8 h + 16 \left(-1\right) = 8 (h + 2 \left(-1\right))
|
-9,356 |
s\cdot 10 + 50\cdot (-1) = 2\cdot 5\cdot s - 2\cdot 5\cdot 5
|
1,553 |
y_1 + i\cdot y - y_2 + i\cdot k = y_1 - i\cdot y + \left(y_2 - i\cdot k\right)\cdot (y_1 - y_2) + y - k = y_1 + y_2 - y - k
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-20,891 |
-9/4 \cdot \frac{7 \cdot (-1) - 8 \cdot l}{-8 \cdot l + 7 \cdot (-1)} = \frac{l \cdot 72 + 63}{-32 \cdot l + 28 \cdot \left(-1\right)}
|
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