id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
4,724 |
(f*q)^3 = 3375 \Rightarrow 15 = f*q
|
-20,802 |
4/1\cdot \tfrac{10\cdot k + 9}{9 + 10\cdot k} = \frac{36 + 40\cdot k}{10\cdot k + 9}
|
-7,712 |
(104 - 28*i + 78*i + 21)/25 = \dfrac{1}{25}*(125 + 50*i) = 5 + 2*i
|
26,922 |
\tfrac{1}{x + Q} \cdot (x - Q) = \frac{x - Q}{Q + x}
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19,674 |
(-d + x)^2 = d^2 + x x - d x\cdot 2
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2,652 |
m^2 - 7 \times m + 10 = m^2 - 6 \times m + 9 - m + 1 = (m + 3 \times (-1))^2 - m + 1 = (m + 3 \times (-1)) \times (m + 3 \times (-1)) - m + 3 \times \left(-1\right) + 2 \times \left(-1\right)
|
-7,062 |
4/39 = 4/13\cdot \frac{1}{12}\cdot 4
|
-10,678 |
-\tfrac{1}{12 + z \times 15} \times (18 \times (-1) + z \times 9) = 3/3 \times \left(-\frac{z \times 3 + 6 \times (-1)}{z \times 5 + 4}\right)
|
17,148 |
A \cdot x/A = x/A \Rightarrow x/A = x
|
11,685 |
\frac{1}{v^2 + 5} + 4 = \frac{1}{v^2 + 5} (1 + 4 (v v + 5)) = \frac{1}{v^2 + 5} (4 v^2 + 21)
|
26,745 |
(2 \cdot n) \cdot (2 \cdot n) = (2 \cdot m)^2 \cdot 2\Longrightarrow n \cdot n = 2 \cdot m \cdot m
|
44,932 |
{6\choose 3} = 20
|
-1,470 |
\frac{1}{7}*2/(1/9*\left(-4\right)) = -9/4*\frac27
|
-15,217 |
\frac{1}{\frac{1}{i^3 a^2} \dfrac{1}{i^8}} = \frac{i^8}{\frac{1}{a^2} \frac{1}{i^3}}
|
-3,024 |
63^{\frac{1}{2}} + 28^{1 / 2} = (9\cdot 7)^{\frac{1}{2}} + (4\cdot 7)^{\frac{1}{2}}
|
-10,515 |
-\frac{6}{15*k}*4/4 = -24/(60*k)
|
2,482 |
(2\cdot \left(-1\right) + x)^2 = (2\cdot (-1) + x)\cdot (2\cdot (-1) + x)
|
11,432 |
3 \cdot x^2 + 3 \cdot x = 3 \cdot (x + x^2)
|
1,167 |
\frac{1}{n + (-1)} r*(n - r)/n = \frac{n r - r r}{n^2 - n}
|
12,618 |
\dfrac{1}{\sqrt{-b + x} (x - a)}(a - b) = \frac{-(-a + x) + x - b}{(x - a) (x - b)} \sqrt{x - b}
|
15,631 |
0 = b\cdot (D + (-1)) + x \Rightarrow -\frac{x}{-D + 1} = b
|
24,613 |
2x^2 = \left(4 + x\cdot 2\right) x - x\cdot 4
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-26,578 |
\left(4 - x*7\right) (4 + x*7) = 4^2 - (7x)^2
|
24,557 |
3*2^3 + 1^3*6 = 30
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36,940 |
b = \dfrac{r}{9 + 10 \cdot m} \implies r = b \cdot 9 + 10 \cdot b \cdot m
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12,379 |
k^2 + 3\times k = k^2 + k + 2\times k = 2\times \binom{k + 1}{2} + 2\times k
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22,454 |
b^2 + a^2 - b \cdot a \cdot 2 = (-b + a)^2
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1,904 |
x_1 + x_2 + 2^{1/2}\cdot (g_2 + g_1) = x_1 + 2^{1/2}\cdot g_1 + x_2 + 2^{1/2}\cdot g_2
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31,961 |
3\times n\times (n + (-1)) = n\times (n + \left(-1\right)) + (n + \left(-1\right))\times n\times 2
|
15,380 |
15 = 5u\Longrightarrow u = 3
|
15,654 |
\binom{n}{r} = \dfrac{n!}{\left(n - r\right)! \cdot r!}
|
10,146 |
\frac12 \cdot (\left(T + B\right)^2 - B^2 - T^2) = T \cdot B
|
-13,086 |
2*\left(-2\right) = \frac{2*\left(-2\right)}{1} = -\frac41
|
16,255 |
\frac{1}{2} + 1/3 + \dfrac{1}{6} + (-1) = 0
|
-476 |
\dfrac{1}{12}\cdot 95\cdot \pi - 6\cdot \pi = 23/12\cdot \pi
|
-5,687 |
\tfrac{1}{2*(-1) + 2*n}*3 = \dfrac{3}{2*\left((-1) + n\right)}
|
34,544 |
6\left(-1\right) + 1 + 2 + 3 + 4 + 5 + 6 = 15
|
-20,983 |
\frac{1}{63}\cdot (x\cdot 35 + 63\cdot (-1)) = \dfrac{1}{9}\cdot (9\cdot (-1) + x\cdot 5)\cdot \frac77
|
11,386 |
x^4 + (-1) = x^4 - x^3 + x^2 \cdot x + \left(-1\right)
|
35,834 |
4 + \sqrt{3} \cdot 2 = 4 + \sqrt{3} \cdot 2
|
13,211 |
30 = \left(63 - 30 p\right) p + (63 - 30 p) p^3 = 63 p - 30 p^2 + 63 p \cdot p \cdot p - 30 p^4
|
4,450 |
6\cdot n \cdot n + n + (-1) = (2\cdot n + 1)\cdot (n\cdot 3 + \left(-1\right))
|
14,358 |
z = x \cdot S \Rightarrow |z|^2 = |S|^2 \cdot |x|^2
|
-20,796 |
-\frac{3}{a*4 + 9}*5/5 = -\frac{1}{20 a + 45}15
|
20,273 |
q^2 + 2xq + (-1) = (\left(1 + x^2\right)^{1 / 2} + q + x) (-(1 + x^2)^{\frac{1}{2}} + q + x)
|
16,573 |
-2^l + 3*2^l + (-1) = (-1) + 2^l*2
|
20,744 |
0 = 2 \beta \Rightarrow 0 = \beta
|
17,597 |
c_2 c_1 = 168 \Rightarrow 168/(c_1) = c_2
|
-3,326 |
-24^{1/2} + 150^{1/2} + 6^{1/2} = \left(25 \cdot 6\right)^{1/2} + 6^{1/2} - (4 \cdot 6)^{1/2}
|
-2,330 |
3/15 - 1/15 = \frac{2}{15}
|
40,940 |
5 \cdot (-1) - 2 \cdot 2 + 9 = -5 + 4 \cdot \left(-1\right) + 9 = 0
|
-9,359 |
-45 \cdot j = -j \cdot 3 \cdot 3 \cdot 5
|
-6,906 |
48 = 3 \cdot 4 \cdot 4
|
13,826 |
\binom{-(R + 1)}{P} = \left(-1\right)^P \cdot \binom{R + P}{P} = (-1)^P \cdot \binom{R + P}{R}
|
-10,448 |
\frac{7}{x \cdot 4 + 2 \cdot (-1)} \cdot 5/5 = \frac{35}{10 \cdot (-1) + 20 \cdot x}
|
1,156 |
1.6^{l + 2*(-1)} + 1.6^{l + 2*(-1)} = 2*1.6^{l + 2*(-1)}
|
11,670 |
7 = \left\lfloor{\frac{1}{6{5 \choose 2}}{30 \choose 2}}\right\rfloor
|
-20,868 |
\dfrac{7}{7}\cdot \frac{2}{1 - a\cdot 8} = \frac{1}{-56\cdot a + 7}\cdot 14
|
15,526 |
2\cdot a\cdot b' + 2 = -a^3 + b'^3\cdot 4
|
6,067 |
\operatorname{atan}(z) = z - \dfrac13\cdot z^3 + z^5/5 - z^7/7 + \dotsm
|
3,336 |
\mathbb{P}(t) = t^4 - 2 t^3 - 6 t t - 2 t + 1 = (t + 1) \left(t t t - 3 t^2 - 3 t + 1\right) = (t + 1)^2 \left(t^2 - 4 t + 1\right)
|
4,521 |
18 = \frac{1}{40} \cdot \left(280 \cdot (-1) + 1000\right)
|
34,756 |
3^{1 / 2}/3 = \frac{1}{3^{\dfrac{1}{2}}}
|
34,091 |
\frac{1}{y \times 1/z} = \frac{z}{y}
|
21,535 |
\sin(A) \sin\left(B\right)*2 = -\cos(A + B) + \cos\left(A - B\right)
|
-12,296 |
\frac{5}{12} = \frac{s}{18 \pi} \cdot 18 \pi = s
|
39,064 |
6.75 = 4 \cdot (12 + 5 + 10) \cdot 0.25 \cdot 0.25
|
13,213 |
\pi/12 = \pi/3 - \tfrac{\pi}{4}
|
9,301 |
x\cdot H_{11} = x\cdot H_{11}
|
51,043 |
\left(-1\right)^3 = -1
|
2,156 |
\frac{1}{\sqrt{8}}*\sqrt{64} = \sqrt{\tfrac{1}{8}*64} = \sqrt{8} = 2*\sqrt{2}
|
4,534 |
3\cdot z^2 + 1 = 4 + ((-1) + z^2)\cdot 3
|
-25,789 |
\frac{4}{40} = \frac{4}{5 \cdot 8}
|
7,005 |
4 \cdot 4 \cdot 4 = 2 \cdot 2\cdot 2^3 + 2^3\cdot 2^2
|
4,751 |
|-2 \cdot y + z| = |2 \cdot y - z|
|
34,470 |
2^n = (1 + 1)^n = \sum_{k=0}^n {n \choose k}*1^{n - k}*1^k = \sum_{k=0}^n {n \choose k}
|
28,311 |
908 = 2 \cdot 2 \cdot 227
|
20,152 |
t_1 \cdot z \cdot t_2 = t_1 \cdot z \cdot t_2
|
-25,813 |
3/60 = \dfrac{3}{10 \cdot 6} \cdot 1
|
-30,595 |
4*(6 + x^2) = 24 + x^2*4
|
-7,251 |
4/15*\frac{1}{16}5 = 1/12
|
24,078 |
( a + h, a - h) = ma + mh + na - nh = ma - nh + na + mh
|
24,735 |
8*r^3 - 12*r^2 + 6*r + (-1) = 16*r^3 - 48*r^2 + 48*r + 16*(-1) = 24*r^3 - 108*r^2 + 162*r + 81*(-1)
|
32,918 |
\dfrac{20}{3} \cdot 1 = 20/3
|
-28,407 |
x^2 - 14*x + 58 = x^2 - 14*x + 49 + 9 = (x + 7*(-1))^2 + 9 = (x*\left(-7\right))^2 + 3^2
|
-27,528 |
16 =2\cdot2\cdot2\cdot2
|
-22,778 |
\dfrac{60}{108}= \dfrac{2\cdot30}{2\cdot54}= \dfrac{2\cdot 2\cdot15}{2\cdot 2\cdot27}= \dfrac{2\cdot 2\cdot 3\cdot5}{2\cdot 2\cdot 3\cdot9}= \dfrac{5}{9}
|
19,349 |
m + 1 = m/1 + m/m
|
5,697 |
\sqrt{\frac14π} = (1/2)!
|
21,833 |
\binom{n}{1 + l} = \binom{n + (-1)}{l} + \binom{n + 2\times \left(-1\right)}{l} + \cdots + \binom{l}{l}
|
19,951 |
d^{l m} = (d^l)^m = (d^m)^l
|
4,157 |
\sec(\tfrac{\pi}{2} - x) = \csc(x)
|
18,086 |
x^2 + (-1)^k*x - \dfrac{1}{4} = 0 \Rightarrow ((-1)^{1 + k} + \sqrt{2})/2 = x
|
-30,916 |
3*b + 6 = 6 + 3*b
|
-1,605 |
\pi*7/6 - \pi/2 = 2/3 \pi
|
14,180 |
x^{t^h} = x \Rightarrow x = (x^{t^{\left(-1\right) + h}})^t
|
18,431 |
\left(6m + 3*(2n + 1) = 9 = 6(m + n) + 3\Longrightarrow 1 = n + m\right)\Longrightarrow m = 1 - n
|
5,196 |
\dfrac1b \cdot \left(-(-y_{i + 1} + y_i) + y_{i + (-1)} - y_i\right) = \frac1b \cdot (y_{(-1) + i} - 2 \cdot y_i + y_{i + 1})
|
-21,052 |
\frac{1}{8}\cdot 4 = \dfrac14\cdot 2\cdot \frac{2}{2}
|
7,577 |
\frac{2\cdot z^2 + z}{z \cdot z + 1} = 1 + \frac{z^2 + z + (-1)}{z^2 + 1} = 1 + \dfrac{2\cdot z^2 + 2\cdot z + 2\cdot (-1)}{2\cdot \left(z^2 + 1\right)}
|
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