id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-4,903 |
3.65\cdot 10 = 3.65\cdot 10/100 = \frac{3.65}{10}
|
222 |
0 = d\cdot 3 + 4\cdot (-1) \Rightarrow \dfrac43 = d
|
52,459 |
\binom{9}{2} \cdot (\binom{7}{2} \cdot 2! \cdot 2! + 3! \cdot 2! \cdot \binom{7}{3} + ... + 7! \cdot 2! \cdot \binom{7}{7}) = 985824
|
-21,046 |
\tfrac33 = 1^{-1} = 1
|
26,080 |
B/C = \frac{B*C/C}{C} = C*B/C/C = \frac1C*B
|
1,872 |
\mathbb{P}(x) = (x + (-1) - 2 \cdot i) \cdot (x + (-1) + 2 \cdot i) = x \cdot x - 2 \cdot x + 5
|
1,099 |
\left(-1\right) + n^2 = (n + (-1)) \cdot \left(n + 1\right)
|
1,774 |
\binom{9}{3}\cdot \binom{6}{3}\cdot \binom{6}{3} = 33600
|
-16,443 |
10\cdot \sqrt{45} = \sqrt{9\cdot 5}\cdot 10
|
-20,018 |
\dfrac{p + 6}{9(-1) + p}*5/5 = \dfrac{5p + 30}{5p + 45 (-1)}
|
21,613 |
\dfrac{1}{2\cdot 4}\cdot (-4 + \sqrt{16 + 64\cdot (-1)}) = \frac{1}{2}\cdot (-1 + \sqrt{-3})
|
5,634 |
\frac{(-1) + k}{l * l} = \tfrac{1/l}{l}*(k + (-1))
|
-6,706 |
8/10 + 1/100 = \dfrac{80}{100} + \dfrac{1}{100}
|
-14,260 |
1 + \dfrac{60}{10} = 1 + 6 = 7
|
997 |
(nx)^2 = n^2 x^2
|
7,181 |
\frac{k + 1}{2 + k} = \frac{1}{2 + k} \cdot (k + 1)
|
-18,364 |
\tfrac{1}{40*(-1) + q^2 - q*3}*(q^2 - 8*q) = \frac{(q + 8*\left(-1\right))*q}{(5 + q)*(8*(-1) + q)}
|
12,764 |
29 = 14*2 + 1
|
-20,361 |
\frac{1}{(-18) \cdot y} \cdot (y \cdot 9 + 90 \cdot (-1)) = \frac99 \cdot \frac{1}{y \cdot (-2)} \cdot (y + 10 \cdot (-1))
|
-4,093 |
6\cdot t^3/5 = 6/5\cdot t^3
|
-25,235 |
\frac{z}{4} = d/dz z^{1/4}
|
3,257 |
E^2\cdot y + 5\cdot y\cdot E + 4\cdot y = (E^2 + E\cdot 5 + 4)\cdot y
|
20,075 |
z + 2 \cdot \left(-1\right) + 1 = z + (-1)
|
32,789 |
k*(1 + x) = x*k + k
|
25,476 |
\frac{1}{9} + 2/15 = 11/45
|
5,667 |
5^2 + 3^2 = 25 + 9 = 34 = r * r\Longrightarrow r = \sqrt{34}
|
-1,219 |
1/5*3/(1/2*3) = 2/3*3/5
|
15,697 |
E\left(\omega_l^2\right) E\left(\omega_k\right) = E\left(\omega_l^2 \omega_k\right)
|
-7,030 |
5/8*\frac19*6*4/7 = 5/21
|
-28,877 |
6+6+6=18
|
19,953 |
z = z/6 + z/12 + z/7 + 5 + \frac12z + 4 \implies z = 84
|
8,934 |
2 \cdot (1 + 2 + \ldots + n) = n \cdot (1 + n)
|
266 |
1 = \left(p + t\right) \times \left(p + t\right) = p \times p + 2\times p\times t + t \times t
|
15,715 |
\cos(-a + a) = \cos(a) \cos(a) + \sin(a) \sin\left(a\right)
|
33,087 |
4+8+8+6 =26
|
26,869 |
\cos{2\cdot y} = -\sin^2{y}\cdot 2 + 1\Longrightarrow \sin^2{y}\cdot 2 = 1 - \cos{2\cdot y}
|
-12,107 |
\dfrac{44}{45} = t/(18\cdot \pi)\cdot 18\cdot \pi = t
|
22,232 |
\frac{1}{26} \cdot 13 \cdot 2 \cdot \frac{12}{25} \cdot 11/24 = \dfrac{11}{50}
|
32,046 |
(1 + q)^2 - (q + (-1))^2 = 4 \cdot q
|
22,613 |
1 + x_0^4 - x_0^2 \cdot 2 = 0 \Rightarrow (x_0 \cdot x_0 + (-1))^2 = 0
|
29,556 |
((-1)\cdot \pi)/2 = -\pi/2
|
11,448 |
\frac{z^{-1/2}}{2} \cdot x = z' \implies x = \frac{1}{z^{-\frac12}} \cdot z' \cdot 2
|
-924 |
0 + 0/10 + 1/100 + 9/1000 + \frac{3}{10000} = \frac{1}{10000} \cdot 193
|
13,519 |
0 = (A, H_i) = AH_i - H_i A
|
31,994 |
93 = 87 \cdot (-1) + 180
|
13,023 |
3 = \dfrac{4!}{2! \cdot 2^2}
|
-23,013 |
50/40 = 5*10/(10*4)
|
19,023 |
1/52 = 4\cdot 13/(52\cdot 52)
|
-22,318 |
\left(3 \cdot (-1) + r\right) \cdot (4 \cdot (-1) + r) = 12 + r^2 - 7 \cdot r
|
10,257 |
1 = (a^2 + h \cdot h + f \cdot f)^2 = a^4 + h^4 + f^4 + 2/4
|
8,159 |
(\dfrac{1}{2}\cdot \sqrt{12})^2 = 3
|
-7,793 |
i \cdot 20/(-4) - 20/(-4) = (i \cdot 20 - 20)/(-4)
|
21,861 |
4\cdot \beta + (-1) = (\sqrt{\beta + 2} + 3\cdot (-1)) \cdot (\sqrt{\beta + 2} + 3\cdot (-1)) = \beta + 2 - 6\cdot \sqrt{\beta + 2} + 9 = \beta + 11 - 6\cdot \sqrt{\beta + 2}
|
6,413 |
2gb = (1 + 1) gb = gb + gb = gb + gb
|
30,337 |
8(-1) + 4\sqrt{3} = 4\sqrt{3} - 8
|
10,633 |
(k + 1)\cdot (k + \left(-1\right)) = k^2 + \left(-1\right)
|
26,769 |
\left(D B\right)^3 = D B D B D B
|
27,473 |
2\cdot \sin\left(E\right)\cdot \cos(E) = \sin(E\cdot 2)
|
18,275 |
y = \tfrac{1}{\frac{1}{y + y} + \frac{1}{y + y}}
|
-10,592 |
-9 = -5 \times y + 4 + 21 \times (-1) = -5 \times y + 17 \times (-1)
|
36,207 |
\frac{\mathrm{d}}{\mathrm{d}x} \tan^3(x) - \tan(x)\cdot 3 + x\cdot 3 = \tan^4\left(x\right)\cdot 3
|
29,483 |
3\cdot z = \dfrac{3\cdot z^3}{z \cdot z}\cdot 1
|
52,222 |
\varphi_1 = \varphi_1
|
31,822 |
2n * n - (-1) + n * n = n * n + 1
|
21,539 |
\operatorname{E}(\theta) + \operatorname{E}(X) = \operatorname{E}(X + \theta)
|
-2,333 |
-\tfrac{4}{11} + \frac{10}{11} = 6/11
|
20,336 |
(f + g)\cdot v_2 + v_1\cdot (f + g) = (f + g)\cdot (v_1 + v_2)
|
22,261 |
g \cdot G_s = g \cdot G_s
|
8,894 |
\frac{x}{2} \cdot \eta \cdot \eta^Z = \eta^Z \cdot \eta \cdot x/2
|
-11,258 |
(y + h) \cdot (y + h) = (y + h) \cdot (y + h) = y^2 + 2 \cdot h \cdot y + h \cdot h
|
17,627 |
Y_2 \cdot Y_1^2 = Y_2 \cdot Y_1 \cdot Y_1
|
-3,664 |
\frac{9}{n^2} \cdot 1/5 = \frac{9}{n^2 \cdot 5}
|
19,440 |
\frac{1}{z^4} + 2\cdot z^2 = \dfrac{1}{z^7}\cdot (z^9\cdot 2 + z^3)
|
10,440 |
\binom{n + 3 + (-1)}{3 + (-1)} = \binom{n + 2}{2} = \frac{1}{2}*(n + 1)*(n + 2)
|
13,388 |
(l + 1)^2 = l^2 + l\cdot 2 + 1
|
18,634 |
e^{1 + |x - y|} = e^{|x - y|} e^1
|
23,805 |
1 + 3 + ... + 2*m + \left(-1\right) = m*(2*m + (-1) + 1)/2 = m^2
|
13,723 |
(\sqrt{A} - \sqrt{B})^2 = A + B - 2 \cdot \sqrt{A \cdot B} = 36 - \sqrt{A \cdot B}
|
-1,646 |
0 + 13/12 \times \pi = \frac{13}{12} \times \pi
|
24,266 |
289 + 1000 \cdot x = 39 + 125 \cdot (2 + 8 \cdot x)
|
29,212 |
y \cdot y + 2\cdot g\cdot y + h = y^2 + 2\cdot g\cdot y + g \cdot g + h - g^2 = (y + g)^2 - g^2 - h
|
32,412 |
-2*n + 2^n = 2^n + 2*(-1) - (n + (-1))*2
|
-23,839 |
4 + \tfrac{40}{8} = 4 + 5 = 4 + 5 = 9
|
3,208 |
\frac{11}{19}*\frac{12}{20} = \dfrac{132}{380}
|
1,018 |
\cos{\theta*2} = 2\cos^2{\theta} + \left(-1\right)
|
7,076 |
6*x_m = m + \left(-1\right) + \sum_{j=m}^6 \left(-x_j + 1\right) \implies m + \sum_{j=m + 1}^6 \left(-x_j + 1\right) = x_m*7
|
3,162 |
\sin(π \cdot 2 + s) = \sin{s}
|
10,368 |
\frac{1}{m} \cdot ((-1) + m) = 1 \Rightarrow m + (-1) = m
|
8,344 |
x\cdot 1/y/z = \frac{x\cdot 1/z}{y}\cdot 1 = x/\left(y\cdot z\right)
|
-4,955 |
45 \cdot 10^{1 + 6} = 10^7 \cdot 45
|
-9,353 |
-44*q = -2*2*11*q
|
23,270 |
1 - \sin^2(\rho) = \cos^2\left(\rho\right)
|
15,572 |
6 + z^2 - 5z = \left(3(-1) + z\right) (z + 2(-1))
|
18,970 |
37 (-1) + (1 + 10)*10/2 = 18
|
7,970 |
x^3 - 1 + x\cdot 3 - x \cdot x\cdot 3 = \left(x + (-1)\right)^2 \cdot (x + (-1))
|
29,382 |
-6*(4*d - 2*f + h) + 2 = 1 \Rightarrow -4*d + 2*f + 1/6 = h
|
7,775 |
n^2\cdot 4 = -(\left(-1\right) + n^2)^2 + (n^2 + 1)^2
|
42,430 |
f^{2^5} = f^{32} = f \cdot f
|
233 |
y \cdot y + x^2 + y \cdot x = (\frac{y}{2} + x) \cdot (\frac{y}{2} + x) + y^2 \cdot 3/4
|
-11,136 |
\left(x + 9*(-1)\right)^2 + b = (x + 9*(-1))*(x + 9*(-1)) + b = x^2 - 18*x + 81 + b
|
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