id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
11,993 |
2*h_1*h_2 + h_1^2 + h_2 * h_2 = (h_1 + h_2)^2
|
-10,705 |
\tfrac{3}{16 + 16\cdot a}\cdot \frac33 = \tfrac{9}{48\cdot a + 48}
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-6,925 |
6 \cdot 8 \cdot 3 = 144
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-4,409 |
\tfrac{1}{x + 4 \cdot (-1)} \cdot 3 + \dfrac{4}{x + 3 \cdot (-1)} = \dfrac{25 \cdot (-1) + 7 \cdot x}{12 + x^2 - 7 \cdot x}
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-11,579 |
12 + 4*i = 4*i + 0 + 12
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25,358 |
\frac{1}{200 \cdot 100} = 1/20000
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49,981 |
\left(\left(\frac{1}{2} = \tan(a) \Rightarrow \cos(a) = 2\sin(a)\right) \Rightarrow \cos^2(a) = 4\sin^2(a) = 4*(1 - \cos^2\left(a\right))\right) \Rightarrow 4 = 5\cos^2\left(a\right)
|
-20,674 |
\frac{z + 6*\left(-1\right)}{6*(-1) + z}*\frac{1}{10}*9 = \tfrac{1}{60*(-1) + z*10}*(54*(-1) + 9*z)
|
34,108 |
s \cdot x = x = x \cdot s
|
39,625 |
2^5\cdot 5 = 160
|
16,895 |
y^{1/k + (-1)} = y^{(1 - k)/k} = (y^{1 - k})^{1/k}
|
937 |
\pi \cdot x \cdot \nu = \nu \cdot x \cdot \pi
|
17,655 |
(\left(-1\right) + 2^4) \cdot 3 = 45
|
-11,831 |
1.952 \times 10^{-2} = 1.952 \times 0.01
|
-13,908 |
2 + 9*8 = 2 + 72 = 2 + 72 = 74
|
-6,213 |
\frac{3}{10*(-1) + z*5} = \tfrac{3}{5*(2*(-1) + z)}
|
-6,254 |
\frac{24}{6\cdot \left(z + 6\cdot (-1)\right)\cdot (3 + z)} = \dfrac66\cdot \dfrac{4}{(z + 3)\cdot (z + 6\cdot \left(-1\right))}
|
22,426 |
x \cdot 2 = 1 + 2 \cdot (-1/2 + x)
|
10,426 |
Q^2\cdot 4 = (1 + Q^2)\cdot 4 + 4\cdot (-1)
|
2,162 |
\frac{1}{4}\cdot (-6\cdot x + 600) = -\frac12\cdot 3\cdot x + 150
|
-20,008 |
\dfrac{2 - f\cdot 4}{2 - f\cdot 4} = \left(2 - 4\cdot f\right)\cdot \frac{1}{-4\cdot f + 2}/1
|
30,809 |
12/16\cdot \frac{11}{15} = \dfrac{1}{240}\cdot 132 = \frac{1}{20}\cdot 11
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-20,830 |
\frac{8}{5*(-1) + x}*7/7 = \dfrac{1}{7*x + 35*\left(-1\right)}*56
|
-3,147 |
4\cdot 13^{1/2} = 13^{1/2}\cdot \left(1 + 3\right)
|
11,924 |
\binom{-1/2}{1} = -\frac{1}{2}
|
25,270 |
x^2 \cdot D = D \cdot x^2
|
-4,521 |
-\frac{5}{x + 1} - \dfrac{4}{x + 4} = \frac{-9 \cdot x + 24 \cdot (-1)}{x^2 + 5 \cdot x + 4}
|
18,080 |
b^{1 + n} = b\cdot b^n
|
-12,042 |
\tfrac{1}{40} \cdot 17 = \frac{1}{10 \cdot π} \cdot s \cdot 10 \cdot π = s
|
22,507 |
\left|{I - H \cdot A}\right| = \left|{-H \cdot A + I}\right|
|
15,712 |
\left(1 + 2 \cdot n\right) \cdot 2 = n \cdot 4 + 2
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14,262 |
41 = 2^6 + 23*(-1)
|
15,141 |
n^4 \cdot 16 = -(-1)^4 + 1 + (n \cdot 2)^4
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-11,056 |
14 = \dfrac{1}{12}\cdot 168
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-28,810 |
\frac12 \times (0 + 100) = \frac{100}{2} = 50
|
-1,602 |
3/4 \pi = -\pi \frac{13}{12} + \pi \cdot 11/6
|
25,343 |
3 \cdot 3 - \dfrac82 = ((-1) \cdot 8)/2 + 9
|
28,437 |
1/\left(gd\right) = 1/\left(dg\right)
|
15,646 |
\frac{x + 2\times (-1)}{4\times \left(-1\right) + x^2} = \frac{1}{x + 2}
|
-23,646 |
4/25 = \frac{4}{5} \cdot 1/5
|
-27,213 |
\sum_{l=1}^\infty \frac{(5 + 3 \cdot (-1))^l}{l \cdot 2^l} = \sum_{l=1}^\infty 1 \cdot \dfrac{2^l}{l \cdot 2^l} = \sum_{l=1}^\infty \tfrac{1}{l}
|
13,348 |
(b + 2*c + d + 2*c)^2 + (d + b)^2 = (c*4 + d + b)^2 + (d + b)^2
|
40,224 |
6 = 7 -1
|
17,238 |
(b*i + a)^{-1} = (i*b + a)^{-1}
|
9,619 |
\sin(x + y) = \sin(x) \cdot \cos(y) + \sin(y) \cdot \cos(x) = \sin(x) + \sin(y)
|
32,470 |
\dfrac14 + s*3/4 = (1 - s)/4 + s
|
36,685 |
e^{y + z} = e^z\cdot e^y
|
21,470 |
\dfrac{1}{49} = \frac{1}{100 + 2 \cdot (-1)} \cdot 2
|
34,135 |
2 x = \left(1 + 1\right) x = x + x = x + x
|
-467 |
\left(e^{\frac{5}{12} i \pi}\right)^{17} = e^{17 \frac{5}{12} \pi i}
|
3,779 |
-x \cdot x + x + 2 = (x + 1) (-x + 2)
|
30,442 |
\frac{\text{d}w}{\text{d}x}\times \frac{\partial}{\partial w} w^m = \frac{\partial}{\partial x} w^m
|
-1,211 |
-8/9 \cdot (-2/9) = \dfrac{1}{(-1) \cdot 9 \cdot 1/8} \cdot (\dfrac{1}{9} \cdot (-2))
|
-20,340 |
\frac{7}{7} \cdot \frac{z \cdot (-5)}{5 \cdot (-1) + z} = \frac{(-35) \cdot z}{35 \cdot (-1) + 7 \cdot z}
|
25,940 |
-T^{x + 1} + I = (-T + I) (I + T + T^2 + \ldots + T^x)
|
31,019 |
\frac{1}{(-1) + y} = \dfrac{1}{(-1) + y}
|
5,965 |
\sum_{k=1}^\infty hk \cdot (-1 + 2(-1))^k = \sum_{k=1}^\infty h \cdot (-3)^k k
|
23,026 |
x^3 + x + 2 = (x + 1) (x^2 + 2x + 2) = (x + 1) \left((x + 1)^2 + 1\right)
|
-10,094 |
\tfrac{-\tfrac{1}{20}*19*1/2}{2} = (-19)/\left(20*2*2\right) = -19/80
|
1,712 |
l - h + l - v + 2\cdot \left(-1\right) = l\cdot 2 + 2\cdot (-1) - h - v
|
-6,565 |
\frac{5}{(y + 9*\left(-1\right))*2} = \dfrac{5}{18*(-1) + 2*y}
|
26,729 |
p \cdot p = (p + 1)\cdot (p + (-1)) + 1
|
36,642 |
8^2 = (-1) + 5*13
|
29,326 |
\dfrac1z = \frac{1}{(1 + (z + 4 \cdot (-1))/4) \cdot 4}
|
28,700 |
\frac{1}{13} \cdot 6 = \dfrac{1}{26} \cdot 12
|
-18,319 |
\frac{1}{x*(7\left(-1\right) + x)}(7(-1) + x) (x + 6(-1)) = \frac{1}{x^2 - x*7}(x^2 - x*13 + 42)
|
39,520 |
32 = 49 \left(-1\right) + 81
|
3,346 |
1 + x^4 - 2x^2 = (x^2 + (-1))^2
|
29,641 |
1 + \lambda^2 + \lambda = 0 \implies \lambda = \dfrac12\left(-1 \pm \sqrt{3} i\right)
|
2,368 |
2 \cdot (-\frac{1}{2} + y) = (-1) + 2 \cdot y
|
37,059 |
(n\cdot 2 + \left(-1\right))\cdot |\frac1n\cdot 6| = 10.5\Longrightarrow n = 4
|
4,565 |
\frac{1}{EA} = \frac{1}{AE}
|
38,090 |
9800 \cdot \dfrac{1}{3}28 = \frac{274400}{3}
|
14,994 |
RM^3 R^X M^3 = R^X M^3 RM^2 \cdot M
|
7,999 |
g \cdot g^{x + 2 \cdot (-1)} = g^{x + (-1)}
|
36,990 |
84 = 21/2\cdot 8
|
25,998 |
((-1) + z)^4 + z^2 \cdot 3 - 6 \cdot z + 5 = ((-1) + z)^4 + 3 \cdot (\left(-1\right) + z) \cdot (\left(-1\right) + z) + 2
|
48,531 |
2 \cdot 2 \cdot 2 + 3^3 = 8 + 27 = 35
|
-4,954 |
\frac{1}{10}\cdot 2.7 = 2.7/10
|
32,341 |
4544 = 4845 + 210\cdot \left(-1\right) + 126\cdot \left(-1\right) + 35
|
26,730 |
5 \cdot 4 = \tfrac{5!}{3!}
|
-1,379 |
-7/9*7/2 = 7*1/2/((-9)*1/7)
|
6,709 |
e^{-a y} = (e^{-y})^a \approx (1 - y)^a
|
24,364 |
(1+x)^{m_1}(1+x)^{m_2} = (1+x)^{m_1+m_2}
|
13,501 |
\tfrac16*5*\pi*34 = \pi*85/3
|
2 |
10 + a^3 + a = (5 + a \cdot a - 2\cdot a)\cdot (a + 2)
|
-5,614 |
\frac{1}{5 \cdot (a + 6)} \cdot 5 = \dfrac{5}{5 \cdot a + 30}
|
-1,180 |
-5/6 \cdot \frac{1}{2} \cdot 9 = \frac{1}{\frac19 \cdot 2} \cdot ((-5) \cdot \dfrac{1}{6})
|
4,007 |
36 = 3^2 \cdot \left(1 + 1\right) \cdot (1 + 1) = 3^2 \cdot \left((1 + 1)^2 + (1 + (-1))^2\right)
|
-3,129 |
(4 + 5)*3^{1 / 2} = 3^{\frac{1}{2}}*9
|
23,610 |
7 \cdot y_1 = -7 \cdot y_2 \Rightarrow -y_2 = y_1
|
2,595 |
n + 2 (-1) = (3 (-1) + n) + 1
|
34,556 |
0 = \theta^4 - 5*\theta^3 + 20*\theta + 16*(-1) = (\theta + (-1))*\left(\theta^3 - 4*\theta * \theta - 4*\theta + 16\right) = (\theta + (-1))*\left(\theta^2 + 4*(-1)\right)*(\theta + 4*(-1))
|
17,878 |
\sinh^2{y} = (\frac12*\left(e^y - e^{-y}\right))^2 = \dfrac{1}{4}*(e^{2*y} + e^{-2*y} + 2*(-1))
|
7,853 |
\frac{1}{1} \cdot \tan{g} = \tan{g}
|
30,628 |
\dfrac{1}{d_1 \cdot d_2} = \frac{1}{d_1 \cdot d_2}
|
6,423 |
e^{-\mathbb{P}(t)} = e^{7\cos\left(t\right)} = e^{7\cos(t)}
|
31,661 |
108^{\frac{1}{2}} + 10 = 10 + 6 \cdot 3^{\dfrac{1}{2}}
|
-20,738 |
\tfrac{-a*8 + 5 (-1)}{a*56 + 35} = -1/7 \dfrac{1}{5 + a*8} (5 + 8 a)
|
12,993 |
2\cdot p = s \Rightarrow p = \frac{s}{2}
|
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