id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-3,793 |
\frac{1}{20} 60 \dfrac{s^3}{s^4} = \frac{60}{20 s^4} s^3
|
-1,783 |
\pi \cdot \frac{31}{12} = 11/6 \cdot \pi + \pi \cdot \frac34
|
25,643 |
5*x + 4*(-1) - x*3 + 1 = 2*x + 5*(-1)
|
21,928 |
\sqrt{5}/2 - \frac{1}{2} = \left(-1 + \sqrt{5}\right)/2
|
-26,536 |
(-y + 4) \times \left(y + 4\right) = 4^2 - y^2
|
-9,661 |
-\dfrac{15}{100} = -0.15
|
39,031 |
76/105 = 1 - \frac13 + 1/5 - \dfrac{1}{7}
|
10,500 |
x \cdot (n + 1) = x \cdot n + x
|
6,034 |
-x^2 + y^2 - x^3 = (-x\cdot (1 + x)^{1 / 2} + y)\cdot ((x + 1)^{\frac{1}{2}}\cdot x + y)
|
19,928 |
d + 2 = 2 + a \Rightarrow a = d
|
-17,508 |
8 = 85 \left(-1\right) + 93
|
17,135 |
12 = 25 + 13 \cdot (-1)
|
7,231 |
b + e + h = h + b + e
|
29,664 |
(-1) + 2 \cdot k = 3 \cdot (-1) + 2 \cdot (1 + k)
|
13,839 |
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 8*\left(8 + 1\right)/2 = \dfrac{2}{2}*4*(2*4 + 1) = 36
|
-3,344 |
2^{1/2} + 32^{1/2} = 2^{1/2} + \left(16\cdot 2\right)^{1/2}
|
-18,958 |
\frac{1}{30} \cdot 13 = \frac{1}{9 \cdot \pi} \cdot A_r \cdot 9 \cdot \pi = A_r
|
29,378 |
A*X^{\dfrac12} = A*X^{1/2}
|
-17,181 |
4 = 4\cdot 3\cdot r + 4\cdot 4 = 12\cdot r + 16 = 12\cdot r + 16
|
36,020 |
\frac{15}{24} = \frac{1}{2 + 7 + 15}15
|
4,416 |
\frac{2\cdot (q + 263)}{2\cdot q + (-1)} = \frac{1}{2\cdot q + (-1)}\cdot (2\cdot q + 526) = 1 + \frac{1}{2\cdot q + (-1)}\cdot 527
|
-20,434 |
(54 + y \times 45)/(-27) = 9/9 \times \left(6 + 5 \times y\right)/\left(-3\right)
|
-7,519 |
57/9 = 19/3
|
41,913 |
6 = \dfrac{1}{20}\cdot 5!
|
18,034 |
\cot{\frac16 \pi} = \sqrt{3}
|
31,982 |
x \cdot 606 = 1010 \cdot x - 404 \cdot x
|
-2,908 |
4^{1/2}\cdot 13^{1/2} - 13^{1/2} = 2\cdot 13^{1/2} - 13^{1/2}
|
10,679 |
\cos\left(y\right) = -\sin\left(y\right)
|
29,474 |
\frac{b + x^3 + x\cdot a}{x + 2} = x^2 - 2\cdot x + a + 4 + \frac{b - 2\cdot (4 + a)}{x + 2}
|
40,089 |
\sinh(t) = \dfrac{1}{2} \cdot (e^t - e^{-t}) = i \cdot \sin(-i \cdot t)
|
20,922 |
\frac{1}{HB}160 = \tan\left(7.9\right) \Rightarrow HB = 160/\tan\left(7.9\right)
|
15,545 |
\tfrac{10}{3} = \frac16 \times (5 + 1 + 2 + 3 + 4 + 5)
|
13,249 |
(-z)^4 = z^4
|
3,552 |
\mathbb{E}(X_1) + \cdots + \mathbb{E}(X_\omega) = \mathbb{E}(X_1 + \cdots + X_\omega)
|
14,942 |
\dfrac{1}{25}\cdot 8 = 3/5\cdot \dfrac{8}{15}
|
14,909 |
\left(kl\right)^2 = k^2 l l
|
11,513 |
\frac{1}{\sec^2(\arctan(v))} = \frac{d}{dv} \arctan(v)
|
11,758 |
(d - g)^2 = -(g + d)^2 + (d^2 + g^2)\cdot 2
|
4,378 |
y \cdot 2 + 5 = y \cdot 2 + 2 + 3
|
23,814 |
0 = -\frac{4}{a \cdot a \cdot a} - 4/a - a + \frac{3b}{a \cdot a} = \frac{1}{a^3}(-4 - 4a^2 - a \cdot a^2 + 3ab)
|
3,705 |
\dfrac{1}{x}*\left(x + 1\right) = \tfrac1x + 1
|
25,320 |
1 - \frac{1}{2} + \frac13 - \frac14 + 1/5 - \frac{\dotsm}{6} = \ln\left(2\right)
|
14,197 |
z\cdot n = -n\cdot (-z)
|
-23,024 |
\dfrac{7 \cdot 4}{9 \cdot 4} = \dfrac{28}{36}
|
24,125 |
\dfrac{0.5^z}{0.7 \cdot 0.3^{z + (-1)}} = 1\Longrightarrow z \approx 1.7
|
12,129 |
2\cdot \dfrac12\cdot \left(5^{1/2} + 3\cdot (-1)\right) + 3 = 5^{1/2}
|
21,679 |
\frac{a}{b \cdot \frac{1}{c}} = a \cdot c/b
|
1,418 |
g! = g*((-1) + g)!
|
40,830 |
z^4 = z^2 z^2
|
23,025 |
(-1) + 2^m = 1 + 2 + \ldots + 2^{(-1) + m}
|
-12,745 |
\frac56 = 15/18
|
30,702 |
a - b - c = -b + a + c
|
-1,491 |
-5/3*\frac{2}{9} = \dfrac{1}{9*1/2}(1/3 (-5))
|
14,307 |
T'/T = -\lambda \Rightarrow 0 = T' + \lambda\cdot T
|
10,355 |
h^2 = \left(4\cdot (-1) + h\right)^2 + (x + 3\cdot (-1))^2\Longrightarrow (x + 3\cdot \left(-1\right))^2 = h^2 - (h + 4\cdot (-1))^2 = 8\cdot h + 16\cdot (-1) = 8\cdot \left(h + 2\cdot \left(-1\right)\right)
|
-23,156 |
-2 = \dfrac{1}{3}*4*(-3/2)
|
-7,817 |
\frac{1 + 21\cdot i}{-3 + 2\cdot i} = \dfrac{-3 - 2\cdot i}{-3 - 2\cdot i}\cdot \frac{1 + i\cdot 21}{2\cdot i - 3}
|
27,807 |
\frac{x^2 + (-1)}{x + (-1)} = \tfrac{1}{x + \left(-1\right)} \times (x + 1) \times (x + (-1)) = x + 1
|
-23,245 |
4/21 = \frac37*\frac19*4
|
-11,992 |
4/9 = \frac{s}{18 \pi} \cdot 18 \pi = s
|
12,658 |
\frac{\text{d}}{\text{d}y} (\cos\left(y\right) + \sin(y)) = \cos(y) - \sin(y)
|
15,691 |
e^{\int P(z)\,\mathrm{d}z} = e^{\int ((-1))\,\mathrm{d}z} = e^{-z}
|
-24,716 |
-55 + 94*i + 13*(-12*i) = -55 + 94*i + 13*(-12*i) = -55 + 13 + 94*i*(-12*i) = -42 + 82*i
|
147 |
2 \cdot 2 + 44 \cdot 44 + 10^2 + 8 \cdot 8 = 2104
|
5,605 |
(e^1 - 1/e)/2 = \sinh{1}
|
31,653 |
\frac{1}{7}\times 60 = \frac{20\times 3}{7}
|
-4,052 |
\dfrac{100}{40 \cdot x} \cdot x = 100/40 \cdot \dfrac1x \cdot x
|
-1,142 |
\dfrac{8}{1/3 \cdot 2} \cdot \frac19 = 3/2 \cdot 8/9
|
9,897 |
z^0 = z^4 \frac{1}{z^2 z^3} z^1
|
9,299 |
u = u - \operatorname{P}(u) + \operatorname{P}\left(u\right)
|
11,467 |
0 = -b + \nu^2 - \nu \Rightarrow (\left(1 + 4*b\right)^{\tfrac{1}{2}} + 1)/2 = \nu
|
17,525 |
22 - 4 \cdot (16 + 21 \cdot (n + (-1)) + \left(-1\right)) = 42 - 84 \cdot n = 21 \cdot (2 - 4 \cdot n)
|
-9,192 |
12 \cdot (-1) - r \cdot 24 = -r \cdot 2 \cdot 2 \cdot 2 \cdot 3 - 2 \cdot 2 \cdot 3
|
14,135 |
\dfrac{2}{5} \cdot π \cdot 1.25 = 2 \cdot π/5 \cdot 5/4 = π/2
|
5,761 |
\sin(-3\cdot x) = -\sin(3\cdot x) = -\sin(x)\cdot (2\cdot \cos(2\cdot x) + 1) = -3\cdot \sin(x)\cdot \cos^2(x) - \sin^3(x)
|
22,600 |
\xi = (\xi + 1)/3 \Rightarrow \xi = \frac12
|
13,256 |
0 = x^3 + A\cdot x + B = -A\cdot x/3 + A\cdot x + B
|
7,059 |
\frac{1}{E \cdot C} = \frac{1}{C \cdot E}
|
27,474 |
2\cdot x\cdot l = 1 \Rightarrow x = \frac{1}{2\cdot l}
|
27,706 |
\dfrac{1}{h/g \cdot g} = g \cdot \frac{1}{g \cdot h}
|
17,271 |
0 = p^{j + (-1)}\cdot a\cdot a = p^{j + \left(-1\right)}\cdot a^2 = p^{j + 2\cdot (-1)}\cdot a\cdot p\cdot a
|
1,177 |
A \times \cos(x - C) = \cos(C) \times \cos\left(x\right) \times A + A \times \sin\left(C\right) \times \sin(x)
|
-530 |
(e^{\frac{\pi i}{12}})^{19} = e^{19 \pi i/12}
|
18,663 |
\frac{1}{2}*(2 + n^2 + n) = {n \choose 0} + {n \choose 1} + {n \choose 2}
|
-20,726 |
10/10 \cdot \tfrac{9 \cdot y}{3 \cdot (-1) + y} \cdot 1 = \dfrac{y \cdot 90}{30 \cdot \left(-1\right) + 10 \cdot y}
|
-4,487 |
x^2 + x \times 2 + 8 \times (-1) = \left(2 \times (-1) + x\right) \times (4 + x)
|
28,058 |
\sin(1 + z) = \sin{1} \cdot \cos{z} + \sin{z} \cdot \cos{1}
|
489 |
x^{17} = x^5\cdot x^2 \cdot x\cdot x^4\cdot x^5
|
-9,977 |
1 = \tfrac{10}{10} = 0*0.01/1 = 100/100 = 1^{-1}
|
-7,601 |
\frac{22\cdot i - 7}{3 - i\cdot 2}\cdot \frac{3 + i\cdot 2}{3 + 2\cdot i} = \frac{-7 + i\cdot 22}{-2\cdot i + 3}
|
6,368 |
\dfrac{1}{X + \frac1X} = \frac{1}{2 \cdot X} = 2/X = 2 \cdot X
|
50,082 |
15=5+5+5
|
29,177 |
0 \geq x + 26^{1/2} rightarrow x \leq -26^{1/2}
|
12,586 |
2/3 + \frac132 = \frac{4}{3}
|
5,889 |
\frac12\cdot (\pi\cdot (-1)) + \pi\cdot 2 = \tfrac{\pi\cdot 3}{2}
|
-20,601 |
-7/5 \frac{1}{6q + (-1)}(q\cdot 6 + (-1)) = \frac{-42 q + 7}{5(-1) + 30 q}
|
28,684 |
\sin{2\cdot s} = x \Rightarrow \frac{\mathrm{d}x}{\mathrm{d}s} = 2\cdot \cos{s\cdot 2}
|
9,370 |
(1 + 2x)^2 + x = (1 + 4x) (1 + x)
|
22,931 |
(y + 5/2) (1 + y \cdot 2) + 1/2 = 3 + 2y^2 + y \cdot 6
|
-30,577 |
-x \cdot x\cdot 3 + 15 = -3\cdot (x^2 + 5\cdot (-1))
|
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