id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
20,783 |
1/55 = \frac{\frac15}{11}
|
28,904 |
\frac{1}{2}*(i + x + 2*(-1))*\left(i + x + \left(-1\right)\right) = \sum_{\theta=1}^{i + x + 2*\left(-1\right)} \theta = \sum_{\theta=2}^{i + x + \left(-1\right)} (\theta + (-1))
|
-15,782 |
-\frac{1}{10} \cdot 53 = -7 \cdot 9/10 + \frac{10}{10}
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-8,065 |
\dfrac{5 + 5 i}{5 + 5 i} \frac{1}{-5 i + 5} \left(45 i + 5\right) = \frac{i \cdot 45 + 5}{-i \cdot 5 + 5}
|
-9,831 |
0.01\cdot (-50) = -50/100 = -\dfrac{1}{2}
|
3,258 |
z \cdot z + \left(-1\right) = (1 + z)\cdot (z + \left(-1\right))
|
12,666 |
z^2 + y\cdot z\cdot 2 + y \cdot y = (z + y)^2
|
-3,828 |
\dfrac{15\cdot x^5}{x^4\cdot 30}\cdot 1 = \frac{15}{30}\cdot \dfrac{x^5}{x^4}
|
14,736 |
\frac{1}{1 + n} + \frac{1}{(n + 1)^2}\cdot \cdots = \frac1n
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-27,487 |
3 \cdot nn \cdot 5 = 15 n^2
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-14,310 |
(5 + 4 - 2*10)*5 = (5 + 4 + 20*(-1))*5 = \left(5 - 16\right)*5 = (5 + 16*(-1))*5 = (-11)*5 = (-11)*5 = -55
|
50,157 |
\sum_{x=1}^\infty \frac{5^x \frac{1}{x^2}}{5^x} = \sum_{x=1}^\infty \dfrac{1}{x^2}
|
390 |
e^{(-1) + 2z}*2 = \frac{\mathrm{d}}{\mathrm{d}z} (e^{2z + (-1)} + 1)
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7,590 |
0 = y \cdot x = z \cdot x^{k + 1} \Rightarrow 0 = z \cdot x^k = y
|
-5,039 |
0.73 \cdot 10^5 = 10^{0\left(-1\right) + 5} \cdot 0.73
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3,752 |
\tfrac{1}{3 + 5}\cdot 3\cdot ((-1)\cdot 0.4 + 1)\cdot 0.4\cdot \frac{8}{8 + 4} = \frac{3}{50}
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-7,589 |
\frac{1}{10} \cdot (2 - 14 \cdot i - 6 \cdot i + 42 \cdot (-1)) = \dfrac{1}{10} \cdot (-40 - 20 \cdot i) = -4 - 2 \cdot i
|
-16,880 |
8 = 20 k^2 + 25 k + 8 \cdot 4 k + 8 \cdot 5 = 20 k^2 + 25 k + 32 k + 40
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31,755 |
|x^2 - 4\cdot x - -3| = |x + 3\cdot \left(-1\right)|\cdot |x + (-1)| \leq 3\cdot |x + (-1)|
|
-20,620 |
\frac{1}{\left(-2\right) \cdot y} \cdot (y \cdot (-2)) \cdot (-\tfrac47) = \frac{y \cdot 8}{y \cdot (-14)}
|
1,479 |
y^2 = 12 z \Rightarrow 4 \cdot (z + 0\left(-1\right)) \cdot 3 = (0(-1) + y)^2
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-24,661 |
3\cdot 2/(2\cdot 4) = \dfrac{6}{8}
|
34,322 |
x^8 + 1 = (x^4 + 1)^2 - 2x^4 = \left(x^4 + 1\right)^2 - (x^2 \sqrt{2})^2
|
8,809 |
\dfrac{1}{z + 1}\cdot (3\cdot z + 2\cdot (-1)) = \frac{1}{z + 1}\cdot (3\cdot \left(z + 1\right) + 5\cdot \left(-1\right)) = 3 - \frac{5}{z + 1}
|
-15,242 |
\dfrac{{(k^{-1}a^{5})^{-2}}}{{(k^{-2}a^{-2})^{4}}} = \dfrac{{k^{2}a^{-10}}}{{k^{-8}a^{-8}}}
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20,746 |
2^5*31 = 992
|
36,669 |
2^{1 / 2} = \frac{7*\dfrac{1}{5}}{(1 - 1/50)^{\frac{1}{2}}}
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-22,921 |
\frac{40}{24} = 2*20/(2*12) = 2*2*10/\left(2*2*6\right) = \frac{2*2*2*5}{2*2*2*3} = \frac13*5
|
24,247 |
\cos{2 \times y} = \cos^2{y} \times 2 + (-1)
|
11,614 |
a \cdot (f + x) = x \cdot a + a \cdot f
|
21,390 |
n \cdot (g + x) = n x + g n
|
16,814 |
\dfrac{1}{s} \times s = s/s
|
23,804 |
\left(p + 1\right)\cdot p^2 = p\cdot p^2 = p^3
|
31 |
\dfrac{0.05}{2} = 0.025
|
53,938 |
\sqrt{2}\zeta^4_{16}\zeta^{4b}_8 = \zeta^2_8(\zeta^a_8 + \zeta^{-a}_8) \implies \sqrt{2}\zeta^{4b}_8 = \zeta^a_8 + \zeta^{-a}_8
|
7,072 |
q\cdot p = s \Rightarrow p = s/q
|
29,467 |
7\cdot \frac{2\cdot 1/100}{1 - \frac{1}{100}\cdot 2} = 7\cdot \tfrac{2}{100 + 2\cdot (-1)} = 7\cdot 2/98
|
4,308 |
{x \choose 2} = \frac{1}{2! \cdot (x + 2 \cdot (-1))!} \cdot x! = (x + (-1)) \cdot x/2
|
39,991 |
\sum_{i=1}^n (n + 1 - 2 \cdot i) \cdot u_i = n \cdot \sum_{i=1}^n u_i + \sum_{i=1}^n u_i - \sum_{i=1}^n 1 \cdot 2 \cdot i \cdot u_i = 0 + 0 - \sum_{i=1}^n 1 \cdot 2 \cdot i \cdot u_i
|
29,422 |
G \cup (B \cap E) = \left(B \cup G\right) \cap (E \cup G) = E \cap (B \cup G)
|
9,458 |
\frac{1}{1 + \tfrac{1}{2\cdot 3 - x \cdot x + \ldots}\cdot x^2}\cdot x = \sin\left(x\right)
|
-6,004 |
\frac{a \cdot 4}{(a + 1) \cdot (5 \cdot (-1) + a)} = \dfrac{4 \cdot a}{a \cdot a - 4 \cdot a + 5 \cdot (-1)}
|
29,538 |
-1 + i = 2\cdot i \Rightarrow i = -1
|
-16,865 |
-8 = -8*\left(-5*h\right) - 40 = 40*h - 40 = 40*h + 40*(-1)
|
22,002 |
\frac12\cdot 630 = 315
|
14,651 |
\frac{x^{n + 1}}{n \cdot x^n} \cdot (n + 1) = \frac{x}{n} \cdot (n + 1) = (1 + 1/n) \cdot x
|
-15,027 |
\frac{1}{m^{20} \cdot \dfrac{m^{10}}{z^{10}}} = \dfrac{\frac{1}{m^{20}}}{\frac{1}{z^{10}}} \cdot \dfrac{1}{m^{10}} = \frac{z^{10}}{m^{30}} = \frac{z^{10}}{m^{30}}
|
-1,822 |
\dfrac{4}{3}*\pi = \pi*\dfrac{1}{12}*13 + \pi/4
|
-19,954 |
0.01 \cdot (-49) = -\frac{1}{100} \cdot 49 = -0.49
|
2,696 |
\frac{\mathrm{d}}{\mathrm{d}x} 1/z = -\frac{1}{z^2}\cdot \frac{\mathrm{d}z}{\mathrm{d}x}
|
20,751 |
Y \cdot S = S^{\frac{1}{2}} \cdot Y^{\frac{1}{2}} \cdot Y^{1/2} \cdot S^{1/2}
|
-3,824 |
\dfrac{q^3}{q \cdot 5}15 = \frac{15}{5} q^2 \cdot q/q
|
34,533 |
{23 \choose 2} = \tfrac{23}{2} 22 = 253
|
9,797 |
\sin{v} = \sin{u}\Longrightarrow v = u
|
-22,832 |
13\cdot 10/(3\cdot 13) = 130/39
|
-11,961 |
4/5 = \frac{1}{6\cdot \pi}\cdot q\cdot 6\cdot \pi = q
|
18,037 |
27.4 = 12/5 + 12/4 + \frac{1}{3}\cdot 12 + \tfrac{1}{2}\cdot 12 + \frac{12}{1}
|
4,601 |
(4 \cdot x \cdot x - 2) \cdot e^{-x^2} = e^{-x^2} \cdot (-2 \cdot x)
|
16,685 |
\dfrac12\cdot (5^{\dfrac{1}{2}} + 3) = (\left(1 + 5^{\frac{1}{2}}\right)/2)^2
|
10,544 |
0 = \frac15(x + w) \Rightarrow x = -w
|
26,317 |
1 + 2 \cdot (-1) + 3 \cdot 3 - 2 \cdot 4 = 0 rightarrow 0 = 0
|
10,361 |
x^2 + 3 - x^2 + 2 \cdot x + 1 = x^2 - x^2 - 2 \cdot x + 3 + \left(-1\right) = -2 \cdot x + 2 = -2 \cdot (x + (-1))
|
-456 |
({ e^{5\pi i / 12}}) ^ {11} = e ^ {11 \cdot (5\pi i / 12)}
|
17,867 |
\binom{5}{3} \cdot 2 = 20
|
30,046 |
z^2 = 4 - -z \cdot z + 4
|
28,902 |
995 \cdot 995 = 990025
|
-23,177 |
1/32 = -\tfrac18 \cdot (-1/4)
|
20,478 |
x^4 + x^2 + 1 = \left(1 + x \cdot x + x\right)\cdot \left(x \cdot x - x + 1\right)
|
44,723 |
12 \cdot 12 = 6 \cdot 24
|
-2,744 |
7\cdot \sqrt{7} = (2 + 5)\cdot \sqrt{7}
|
13,823 |
b^4 - g^4 = (b^2 - g^2) (b^2 + g * g) = \left(b - g\right) (b + g) \left(b^2 + g^2\right)
|
22,991 |
x^2 + 2*d^2 = 0\Longrightarrow x = d = 0
|
-17,039 |
6 = 6\cdot \left(-2\cdot n\right) + 6\cdot 4 = -12\cdot n + 24 = -12\cdot n + 24
|
-17,864 |
71 + 6 \times (-1) = 65
|
-6,527 |
\frac{5}{4 \cdot m + 12 \cdot (-1)} = \frac{1}{4 \cdot (m + 3 \cdot (-1))} \cdot 5
|
19,739 |
\left(-\sqrt{-5} + 1\right)\cdot (1 + \sqrt{-5}) = 2\cdot 3
|
40,930 |
y\times 3^0 = y
|
28,768 |
e\cdot g + f\cdot h = g\cdot e + h\cdot f
|
-25,238 |
\frac{d}{dx} \frac{1}{x^4} = -\frac{1}{x^5}*4
|
3,128 |
\frac{1}{10} = \frac{1}{5} \cdot 3 \cdot \dfrac{2}{4}/3
|
-2,116 |
\dfrac{23}{12}*\pi - \pi*\frac54 = 2/3*\pi
|
19,445 |
1 - x^{n + 1} = -(x^{n + 1} + (-1))
|
10,554 |
\frac{1}{13} + \frac{1}{13*1/12} = \frac{12}{13} + 1/13 = 1
|
31,793 |
z^3 + x \cdot x^2 = (x^2 - zx + z^2) (z + x)
|
23,386 |
\frac{-1 + 5*\left(-1\right)}{-2 + 4*(-1)} = -\frac{6}{-6} = 1
|
11,192 |
\dfrac{1}{11} \cdot 6 \cdot \frac{7}{12} = 42/132
|
2,279 |
\frac{1}{y + R}\times x^2 = (2\times x)^2\times \frac{1}{y + R}/4 \geq (4\times x - y - R)/4
|
10,047 |
1 - \frac{1}{2^{32}} = \dfrac{1}{2^{32}}\cdot ((-1) + 2^{32})
|
2,091 |
x+\alpha=x+\frac{\alpha}{2}+\frac{\alpha}{2}
|
43,411 |
\left(b_{1 + x} = \sqrt{b_x \cdot a_x} rightarrow \lim_{x \to \infty} b_{x + 1} = \lim_{x \to \infty} \sqrt{a_x \cdot b_x}\right) rightarrow \sqrt{\lim_{x \to \infty} a_x \cdot \lim_{x \to \infty} b_x} = \lim_{x \to \infty} b_{x + 1}
|
22,003 |
\frac{30/31}{30} + \dfrac{1}{31} = \frac{2}{31}
|
20,000 |
l^{f_2 + f_1} = l^{f_2} l^{f_1}
|
23,031 |
\left(\frac{g^2}{b^2} = 2 \Rightarrow g^2 = b^2\cdot 2\right) \Rightarrow g = b\cdot \sqrt{2}
|
2,379 |
a*7 = 2*\left(1 + a\right) + a*5 + 2*\left(-1\right)
|
24,079 |
V \cdot V + (-1) = (1 + V) \cdot (V + (-1))
|
47,144 |
105=3\cdot 5 \cdot 7
|
21 |
3 (-1) + 37 + 31 (-1) + 21 + 19 (-1) + 17 (-1) + 13 + 11 + 7 \left(-1\right) + 5 = 10
|
-12,754 |
8*(-1) + 22 = 14
|
24,042 |
2^{\frac13} = (2^{1/9})^3
|
8,284 |
42 (-1) - 10 y^2 - y = -y*(y^2 - 2 y + 1) + y^3 - y^2*12 + 42 (-1)
|
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