id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-7,197 |
2/7*\frac17*3 = \frac{6}{49}
|
24,625 |
\mathbb{P}(z) := 27 \cdot (-1) + z^6 + 10 \cdot z^3 := \left(z^3\right)^2 + 10 \cdot z^3 + 27 \cdot \left(-1\right)
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-161 |
\dfrac{5!}{2!\cdot 3!} = \binom{5}{3}
|
11,623 |
-(4 + x \cdot x - 4 \cdot x) \cdot 7 + 4 = -7 \cdot x \cdot x + x \cdot 28 + 24 \cdot \left(-1\right)
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24,018 |
\cos{3x} = -\cos{x}*3 + 4\cos^3{x}
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-1,922 |
19/12\cdot π + π/2 = 25/12\cdot π
|
23,033 |
(1 - \frac{z}{x}) \cdot \left(\sqrt{z^2 + x^2}\right)^2 = (z^2 + x^2) \cdot (1 - \dfrac{z}{x})
|
10,772 |
z^2 - 2 \cdot z = \left(-1\right) + ((-1) + z)^2
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18,009 |
x^2/(\sqrt{x}) = \sqrt{\dfrac{x^4}{x}} = \sqrt{x^3}
|
43,273 |
{7 \choose 3} = 7 \cdot 5
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-4,527 |
x * x + x + 2(-1) = ((-1) + x) (2 + x)
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31,788 |
(a - b) \cdot (a^2 + b \cdot a + b^2) = -b^3 + a^2 \cdot a
|
26,966 |
1 - 2*z + z^2 = (-z + 1)^2
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26,995 |
20 \sqrt{2 - \sqrt{3}} = \sqrt{-\sqrt{3} \cdot 400 + 800}
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16,655 |
k^2 + m^2 = -m \cdot k \cdot 2 + (k + m)^2
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23,181 |
1/(102*101) = 1/10302
|
13,381 |
2 + x * x + 3*x = \left(1 + x\right)*(2 + x)
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11,883 |
\frac{\pi}{6} = \sin^{-1}{\dfrac12}
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23,739 |
x^2 \cdot 6 + x \cdot 11 + 35 \cdot \left(-1\right) = (3 \cdot x + 5 \cdot (-1)) \cdot (x \cdot 2 + 7)
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-11,040 |
\frac{176}{8} = 22
|
13,135 |
-(-H)^{n + 1} = -(-1)^{n + 1}*H^{n + 1} = (-1)^{n + 2}*H^{n + 1}
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-19,589 |
\frac{1/5*9}{\frac{1}{6}} = \frac15*9*\frac61
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4,254 |
z^3 + z * z + z + 3*(-1) + 3*z^2 + z*5 + 4 = z^3 + z^2*4 + 6*z + 1
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-20,362 |
\frac{1}{-9 \cdot q + 2} \cdot 1 = \frac{7}{14 - 63 \cdot q}
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21,468 |
9 + s^2 + s*2 = (1 + s)^2 + 8
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-20,119 |
\frac{10}{3}\cdot \frac{n + 2}{2 + n} = \frac{1}{n\cdot 3 + 6}\cdot (n\cdot 10 + 20)
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15,585 |
(4/10)^4 = \left(2/5\right)^4 = \dfrac{16}{625}
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21,904 |
\mathbb{E}(A B) = \mathbb{E}(A) \mathbb{E}(B)
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-8,107 |
3\cdot 4 = 12
|
-20,764 |
\frac{1}{x \times 7 + 28} \times (49 + 7 \times x) = \frac{x + 7}{4 + x} \times \frac17 \times 7
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-20,213 |
9/9 \frac{1}{9} (6 \left(-1\right) + z\cdot 10) = (54 (-1) + 90 z)/81
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-5,238 |
\frac{9.8}{10} = \frac{9.8}{10} \cdot 10^4 = 9.8 \cdot 10 \cdot 10^2
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-11,100 |
(x + 6)^2 + f = (x + 6)\cdot \left(x + 6\right) + f = x^2 + 12\cdot x + 36 + f
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21,838 |
x + 1 = x \cup x = \left\{m \in \mathbb{N}\; \middle|\; m < n \right\}
|
6,516 |
8 + k^2*9 + 9(-1) = (-1) + 9k^2
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6,070 |
\dfrac{1}{A} - \frac1B = \dfrac{1}{B\times A}\times (B - A)
|
9,105 |
1^5 + 2^5 + 3^5 + 4^5 + 1^7 + 2^7 + 3^7 + 4^7 = 2*(1 + 2 + 3 + 4)^4
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38,155 |
a*1/b/x = a/(b*x) = a*1/b/x = \frac{a}{b*x}
|
10,427 |
(x + (-1))*(1 + x + \dotsm + x^{n + (-1)}) = x^n + (-1)
|
-19,536 |
\frac{9 \cdot 1/2}{1/9 \cdot 2} = 9/2 \cdot 9/2
|
15,310 |
E_1 \cdot A_0 + A_1 \cdot E_0 = (A_1 + A_0) \cdot \left(E_1 + E_0\right) - A_0 \cdot E_0 - E_1 \cdot A_1
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-18,446 |
4 \cdot x + 6 = 3 \cdot (x + 2 \cdot \left(-1\right)) = 3 \cdot x + 6 \cdot (-1)
|
50,772 |
{21 \choose 7} = {21 \choose 14}
|
44,571 |
(2) \implies (3) \implies (4)
|
14,991 |
b^2 + c^2 - bc > bc \Rightarrow b^3 + c^3 > bc*(b + c) = b * b c + bc * c
|
24,524 |
\frac{1}{7}360 = \dfrac{1}{70}*3600
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-6,179 |
\frac{4}{s*4 + 16} = \frac{1}{(4 + s)*4}*4
|
-20,190 |
\tfrac{100 + p \cdot 10}{40 \cdot p + 60 \cdot \left(-1\right)} = \frac{10}{10} \cdot \tfrac{p + 10}{6 \cdot (-1) + p \cdot 4}
|
14,755 |
\left|{Y\times X + I}\right| = \left|{X\times Y + I}\right|
|
18,690 |
12-6+1=7
|
13,775 |
\omega^2 = (-\omega)^2
|
-15,998 |
-85/10 = \tfrac{1}{10}5 - 10*9/10
|
-20,089 |
\frac{-3\times t + 3}{5\times (-1) + 5\times t} = \frac{(-1) + t}{t + \left(-1\right)}\times \left(-3/5\right)
|
18,565 |
25/4 = \frac52\cdot \frac{1}{2}\cdot 5
|
13,238 |
c^2 - d^2 = (c + d) \cdot \left(c - d\right)
|
19,152 |
\sin(c) \cos\left(c\right)\cdot 2 = \sin(c\cdot 2)
|
1,870 |
(s + 1) \times (1 - t) = 1 + s - t - s \times t
|
21,466 |
1/(f_2\cdot f_1) = \dfrac{1}{f_2\cdot f_1}
|
25,209 |
300 = (9 + 6 (-1))*10*10
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-30,857 |
\frac{1}{x + 1}\cdot (x^4 + x^3\cdot 2 + x^2) = x^3 + x^2
|
-29,331 |
9 - i \cdot 2 = 1 + 8 - 2i
|
20,355 |
\frac{k+1}{2}\cdot2=k+1
|
-22,702 |
\frac{45}{54} = \dfrac{5 \cdot 9}{9 \cdot 6}
|
-2,261 |
1/11 = -\frac{6}{11} + \dfrac{7}{11}
|
23,496 |
\cos{z} \cdot \sin{t} - \cos{t} \cdot \sin{z} = \sin\left(-z + t\right)
|
13,384 |
5 + x + x^2 + \dotsm*\dotsm = 5 + \tfrac{x}{1 - x}
|
41,084 |
e^A\times e^Y = e^{A + Y} = e^Y\times e^A
|
-7,505 |
5 = 45/9
|
-23,114 |
-4/3\cdot 8/3 = -32/9
|
726 |
\left(1 + 1/n\right)^{1 + n} = \left((n + 1)/n\right)^{1 + n}
|
30,239 |
a \cdot \frac{b}{c} = a \cdot b/c
|
16,691 |
V x_f = V x_f
|
38,672 |
\binom{r}{x} = \binom{r + (-1)}{x + (-1)}*r/x
|
6,327 |
\cos(\pi\cdot 4 - w) = \cos(\pi\cdot 2 - w)
|
28,836 |
-1 \cdot 1 + 7^2 = 8^2 - 4^2
|
36,191 |
1^2 + 2 * 2 = 5^1
|
-26,409 |
\tfrac{z^n}{z^m} = z^{n - m}
|
8,213 |
10^h = 5^h \cdot 2^h
|
35,584 |
\left\lfloor{100/5}\right\rfloor + \left\lfloor{100/25}\right\rfloor + 0 = 24
|
-10,626 |
\dfrac15*5*(-9/(s*3)) = -45/(15*s)
|
25,501 |
\|u\| = \|u - u_x + u_x\| \leq \|u - u_x\| + \|u_x\|
|
27,298 |
( a_2*a_1, h_1*h_2) = ( a_1*a_2, h_2*h_1)
|
5,481 |
4 \cdot \left(-1\right) + x \cdot x - 3 \cdot x = (4 \cdot \left(-1\right) + x) \cdot (1 + x)
|
15,383 |
(\sqrt{a} + \sqrt{b})^3 - (3a + b)(\sqrt{a} + \sqrt{b}) = 2(b-a)\sqrt{a}
|
32,894 |
14114 = 22^3 + 3^3 + 4 * 4 * 4 + 15^3
|
-14,320 |
\frac{1}{7 + 3 \cdot (-1)} \cdot 28 = 28/4 = \frac{1}{4} \cdot 28 = 7
|
-30,282 |
z + \left(-1\right) + \frac{7}{z + 2 \cdot (-1)} = \frac{1}{z + 2 \cdot (-1)} \cdot (9 + z \cdot z - z \cdot 3)
|
303 |
\frac{1}{y^2 + 3}*(y^2 + 1) = \tfrac{y^2 + 3 + 2*(-1)}{y^2 + 3} = 1 - \frac{2}{y^2 + 3}
|
-7,767 |
\frac{1}{34} \cdot (-200 - 50 \cdot i - 120 \cdot i + 30) = \left(-170 - 170 \cdot i\right)/34 = -5 - 5 \cdot i
|
25,048 |
\left|{Y_1\cdot Y_2}\right| = \left|{Y_1}\right|\cdot \left|{Y_2}\right| = \left|{Y_2}\right|\cdot \left|{Y_1}\right| = \left|{Y_2\cdot Y_1}\right|
|
-9,379 |
-k\cdot 6 + 3 = -k\cdot 2\cdot 3 + 3
|
19,295 |
\dfrac{1}{2^{1/2}} = \sin{3*\pi/4}
|
-1,682 |
3/4\cdot \pi + \dfrac{\pi}{2} = 5/4\cdot \pi
|
18,188 |
d/dx \operatorname{asin}(x) = \tfrac{1}{(1 - x \cdot x)^{\frac{1}{2}}}
|
-17,822 |
67 + 62\times \left(-1\right) = 5
|
21,833 |
{n \choose k + 1} = {n + (-1) \choose k} + {n + 2 \times \left(-1\right) \choose k} + \dotsm + {k \choose k}
|
30,315 |
e^{1.2} \gt 1 + 1.2 + 1.2^2/2 + \dfrac16 1.2 1.2^2 = 3.208 > 3.2
|
13,145 |
T \cdot L = A \Rightarrow det\left(A\right) = det\left(L \cdot T\right) = det\left(L\right) \cdot det\left(T\right)
|
13,295 |
(x + 1)^n*(x + 1)^n = (1 + x)^{n*2}
|
11,660 |
B\times y = B\times y
|
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