id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
5,250 |
1 + 2^0 + 2^1\cdot ...\cdot 2^{P + (-1)} + 2^P = 2\cdot 2^P = 2^{P + 1}
|
7,596 |
\frac{1}{12} + \frac{1}{16} = \dfrac{4}{48} + \dfrac{3}{48} = 7/48
|
17,492 |
\sin^2 x = 1/\csc^2 x
|
-15,191 |
\frac{1}{\frac{k}{a^2}\cdot \frac{1}{a^9\cdot k^{15}}} = \frac{a^9\cdot k^{15}}{\frac{1}{a^2}\cdot k}\cdot 1
|
-7,768 |
\left(-20 + 4\times i + 20\times i + 4\right)/8 = \left(-16 + 24\times i\right)/8 = -2 + 3\times i
|
-1,509 |
\frac56*9/2 = \dfrac{9*1/2}{6*\frac{1}{5}}
|
14,804 |
5/27 = 1/9 + \frac{4}{18}\cdot \frac13
|
-15,080 |
\tfrac{p^5}{l^2\cdot p^4} = \dfrac{1}{(p^2\cdot l) \cdot (p^2\cdot l)\cdot \dfrac{1}{p^5}}
|
-29,370 |
\left(7 + y\right)\cdot \left(7 - y\right) = 7^2 - y^2 = 49 - y \cdot y
|
46,413 |
e^0 = 1 > 0
|
3,383 |
-y^3 + z z z = (-y + z) (z^2 + z y + y^2)
|
9,966 |
\frac{1}{-q + 1}\cdot (-q^{x + 1} + 1) = \frac{-q^{x + 1} + 1}{-q + 1}
|
-4,213 |
\dfrac{1}{l^3} \cdot l^2 \cdot l \cdot 12 \cdot 12/(12) = 144/12 \cdot \tfrac{l \cdot l \cdot l}{l^2 \cdot l}
|
42,103 |
3 \cdot 3^2 + 3^3 + 3^3 = 81
|
24,227 |
(-1) + x^{10} = (x + (-1))\cdot (1 + x)\cdot (x^8 + x^6 + x^4 + x^2 + 1)
|
5,925 |
3*6*4 = 72 = 6 * 6 + 6^2
|
36,859 |
n^2 = 36 + (6 + n)\cdot \left(n + 6\cdot (-1)\right)
|
-489 |
e^{20 \cdot 3 \cdot \pi \cdot i/4} = (e^{\frac{1}{4} \cdot \pi \cdot 3 \cdot i})^{20}
|
22,952 |
\sin(\pi/3) = \frac{3^{1/2}}{2}
|
-11,798 |
\left(2/9\right)^2 = \frac{1}{81}\cdot 4
|
-20,041 |
\dfrac{-9}{5} \times \dfrac{3t + 2}{3t + 2} = \dfrac{-27t - 18}{15t + 10}
|
-502 |
-24 \pi + \pi*49/2 = \dfrac12\pi
|
19,722 |
(k + 1)! \cdot k = (k + 1 + 1)! + 1 = \left(k + 2\right)! + (-1)
|
24,116 |
\dfrac{(1 - z) e^{z + \left(-1\right)}}{((-1) + z)*2} = -e^{(-1) + z}/2
|
-14,513 |
\dfrac{1}{8 + 6\cdot (-1)}\cdot 6 = 6/2 = \dfrac{1}{2}\cdot 6 = 3
|
-10,559 |
8/(25*z)*3/3 = 24/(75*z)
|
7,181 |
\frac{1}{i + 2}\cdot (i + 1) = \frac{i + 1}{i + 2}
|
6,538 |
k\cdot 2 + (-1) = ((-1) + 2)\cdot \left(2\cdot k + (-1)\right)
|
-2,660 |
\sqrt{11} + 4\times \sqrt{11} = \sqrt{16}\times \sqrt{11} + \sqrt{11}
|
-10,377 |
-\frac{6 \cdot (-1) + y}{y + 3 \cdot (-1)} \cdot 2/2 = -\frac{1}{6 \cdot (-1) + y \cdot 2} \cdot \left(2 \cdot y + 12 \cdot (-1)\right)
|
-3,184 |
5^{1 / 2} = (3 \cdot (-1) + 4) \cdot 5^{1 / 2}
|
-18,335 |
\frac{1}{l \cdot (l + 6)} \cdot \left(l + 6\right) \cdot (l + 10 \cdot (-1)) = \frac{1}{l \cdot l + 6 \cdot l} \cdot (l \cdot l - 4 \cdot l + 60 \cdot (-1))
|
-6,344 |
\dfrac{4}{2(6 + x) \left(8 + x\right)} = \tfrac22*\frac{2}{(8 + x) \left(6 + x\right)}
|
24,648 |
\pi - \frac{\pi}{8} = \dfrac{7*\pi}{8}
|
-5,616 |
\frac{4}{2 \cdot (y + 6 \cdot (-1)) \cdot (y + 5)} = \tfrac{1}{2} \cdot 2 \cdot \frac{2}{(y + 5) \cdot (6 \cdot (-1) + y)}
|
-15,121 |
\tfrac{(\tfrac{1}{n^4})^3}{\left(\tfrac{1}{p^4}\cdot n\right)^5} = \frac{1}{\dfrac{n^5}{p^{20}}\cdot n^{12}}
|
43,839 |
\alpha \cdot \alpha = \alpha^2
|
-4,211 |
\frac{144}{x * x^2*12}*x^3 = \frac{1}{x * x^2}*x^2 * x*\dfrac{144}{12}
|
36,842 |
\cos^2\left(x\right) = 1 - \sin^2\left(x\right)
|
17,701 |
1^2 + 2 \times 2 + 3^2 + 4 \times 4 + 5^2 + 6 \times 6 = 91
|
-6,524 |
\frac{4}{4(9(-1) + x) \left(5(-1) + x\right)} = \frac{4*\frac14}{(x + 9(-1)) (x + 5(-1))}
|
42,226 |
3 * 3 * 3 + 4*3 * 3 + 14*3 + 9 = 8 + 17 + 4 + 9 = 0
|
-29,867 |
x \cdot x \cdot x\cdot 8 + 3\cdot x \cdot x + 6\cdot x = d/dx (3\cdot x^2 + 2\cdot x^4 + x \cdot x^2)
|
-1,634 |
-7/4\cdot \pi + \pi = -\pi\cdot 3/4
|
-9,430 |
x \cdot 2 \cdot 2 \cdot 2 \cdot x + 2 \cdot 2 \cdot 2 \cdot x = x^2 \cdot 8 + 8 \cdot x
|
-6,640 |
\tfrac{4}{(t + 10 \cdot \left(-1\right)) \cdot 2} = \frac{4}{20 \cdot (-1) + 2 \cdot t}
|
3,297 |
2 \times x^2 - 2 \times x + 1 = x^2 + x^2 - 2 \times x + 1 = x \times x + (x + (-1))^2
|
31,827 |
-9 = 4 (-1) + 35 + 60 (-1) + 20
|
10,756 |
\frac{v}{d} - \dfrac{d}{g'} \frac{v}{d} = -v/g' + \frac{v}{d}
|
5,823 |
V^2\cdot V \cdot V\cdot V^2 = V^6 = V^3\cdot V^3
|
30,970 |
m = 2\cdot 2\cdot m/4
|
3,904 |
-2e + 4 = -e\cdot 2 + 5 + (-1)
|
15,995 |
-2\cdot \operatorname{atan}(R) = \operatorname{atan}(-R) - \operatorname{atan}(R)
|
2,199 |
0 = 3 - z*2 - y \Rightarrow 3 - 2 z = y
|
-25,875 |
\frac{g^7}{g^6} = g^{7 + 6 \cdot (-1)} = g^1
|
-27,492 |
11*c*c*c = c^3*11
|
5,617 |
d_{u + 2(-1)} d_{u + (-1)} = d_u^2 \Rightarrow d_{u + (-1)} d_{u + 2\left(-1\right)} d_u = d_u^3
|
8,797 |
2 \cdot \alpha + 1 + 2 \cdot \beta = (\alpha + \beta) \cdot 2 + 1
|
-11,639 |
7 + 9 \cdot i = 2 + 5 + i \cdot 9
|
-7,818 |
\frac{-i*10 + 5}{-3*i + 4} = \frac{1}{4 - i*3}*(5 - 10*i)*\tfrac{4 + 3*i}{4 + 3*i}
|
16,263 |
1 = \frac1a + \frac{1}{a + f} + \frac{1}{a + f + c} \geq \dfrac{1}{a + f + c}\cdot 3
|
12,835 |
z^3 = z^2 + z + 2 \cdot \left(-1\right) + 2 \cdot \sqrt{1 + z^3 - z^2 - z} \implies (z^2 \cdot z - z^2 - z + 2)^2 = 4 \cdot (z \cdot z \cdot z - z^2 - z + 1)
|
51,244 |
\frac{(3 n + 4)!*7^{-(n + 1)}}{\frac{(3 n + 1)!}{n! \left(2 n + 1\right)!}*7^{-n}} \frac{1}{(n + 1)! \left(2 n + 1\right)!} = \frac{7^{-1 - n} n! (2 n + 1)! (3 n + 4)!}{(n + 1)! (2 n + 3)! (3 n + 1)!*7^{-n}} 1 = \dfrac{(3 n + 4)! (2 n + 1)!}{(n + 1)*7 (2 n + 3)! (3 n + 1)!}
|
2,684 |
\frac17*3/4 + 4/7*0 = 3/28
|
-6,697 |
\frac{5}{100} + \frac{7}{10} = 70/100 + \frac{5}{100}
|
-10,332 |
-\tfrac{30}{r \times 50} = 10/10 \times \left(-\frac{3}{r \times 5}\right)
|
32,600 |
\frac{1}{M \cdot N} \cdot 2 = \dfrac{1}{N \cdot M} = N^T \cdot M^T = (M \cdot N)^T
|
-28,795 |
\frac{2\cdot \pi}{\frac13\cdot \pi\cdot 2} = 3
|
24,911 |
10 = 368 \cdot (-1) + 378
|
6,845 |
(-1) \cdot (-2) \cdot 2 = (-2) \cdot \left(-2\right)
|
37,986 |
\sqrt{k!} \sqrt{k!} = k!
|
23,178 |
\frac{86}{100}*\dfrac{114}{100} = \frac{1}{10000}9804 \lt 1
|
34,521 |
a^{W + m} = a^m a^W
|
-11,535 |
-2\cdot i + 23 = 15 + 8 - i\cdot 2
|
3,751 |
x + 8 - 6\cdot \sqrt{x + (-1)} = x + (-1) - 6\cdot \sqrt{x + (-1)} + 9 = (\sqrt{x + (-1)} + 3\cdot (-1))^2 = \left(3 - \sqrt{x + (-1)}\right)^2
|
49,960 |
x - y = x - y
|
-8,901 |
-1^5 = (-1) \cdot \left(-1\right) \cdot (-1) \cdot (-1) \cdot (-1)
|
30,115 |
280/13 = \frac{1}{13}2 \cdot 7/3 \cdot 60
|
24,309 |
(T_1 + T_2) \cdot (T_1 + T_2) - \left(T_1 - T_2\right)^2 = 4 \cdot T_1 \cdot T_2
|
27,431 |
V_l/(C_l) = \frac{d_l \cdot V_l}{d_l \cdot C_l} = d_l/(C_l) \cdot V_l/(d_l)
|
-16,607 |
6 \cdot \sqrt{16 \cdot 11} = \sqrt{176} \cdot 6
|
25,389 |
1 = \dfrac{1}{3} + \tfrac13 + \frac13
|
29,788 |
c^2 \cdot a = |c \cdot c \cdot a| = 2/3 \cdot |c|^3 + |a|^3/3
|
27,261 |
p^4 - 2p^2 + 1 = (p^2 + (-1))^2
|
-23,827 |
3 + \frac{1}{4}*4 = 3 + 1 = 4
|
36,349 |
\frac{1}{1.5 + 2}\cdot 1.5 = \dfrac37
|
18,950 |
Y\times \frac{e^x}{Y} = e^{Y\times \dfrac1Y\times x}
|
13,726 |
\frac{h_2}{b*1/(h_1)} = h_2*\frac{h_1}{b}
|
13,301 |
\binom{\nu + (-1)}{2} + 1 = \binom{\nu}{2} - \nu + 2(-1)
|
-26,477 |
70 \times x = 2 \times 5 \times x \times 7
|
-11,968 |
\dfrac{14}{45} = s/(6*\pi)*6*\pi = s
|
1,794 |
((-1) + a)\cdot \left(a + 1\right) = \left(-1\right) + a \cdot a
|
6,343 |
BA + 0 = BA
|
4,433 |
\frac{\frac14}{-\frac{1}{4} + 1} = \dfrac13
|
-6,003 |
\frac{3}{35 + x \cdot 5} = \frac{3}{\left(x + 7\right) \cdot 5}
|
2,341 |
r\cot(r) = 1 - r^2/3 - \frac{r^4}{45 ...} \approx exp(((-1) r^2)/3) (1 - \frac{1}{90 r^4}7 + ...)
|
33,702 |
c_2\cdot c_3 = c_3\cdot c_2
|
11,313 |
-2^n\cdot (n + 2\cdot (-1)) - 2 = ((-1) + 2^n)\cdot 2 - n\cdot 2^n
|
23,360 |
3{k + 1 \choose 4} = {{k \choose 2} \choose 2}
|
2,365 |
y_n y/y = y_n
|
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