id
int64 -30,985
55.9k
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stringlengths 5
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|---|---|
-4,302 |
\frac{p*36}{72*p^3} = \frac{p}{p^3}*\frac{1}{72}*36
|
16,580 |
\frac{y}{15}\cdot 2 = y\cdot 2/15
|
4,719 |
a^3 - d^3 = \left(d^2 + a^2 + d \cdot a\right) \cdot \left(a - d\right)
|
8,689 |
1 + z^{\frac13} = 0 rightarrow z^{\tfrac{1}{3}} = -1
|
23,985 |
5^7\cdot 2 + 2\cdot 5^5 + 2\cdot 5^6 = 193750
|
3,535 |
0 \cdot \binom{n}{0} + \binom{n}{1} + 6 \cdot \binom{n}{2} + 6 \cdot \binom{n}{3} = n^3
|
42,368 |
\int \dfrac{\cot(u)}{\sin(u)}\,du = \int \csc(u) \cdot \cot(u)\,du = -\csc(u)
|
-427 |
(e^{\frac16 \cdot π \cdot i \cdot 5})^9 = e^{\frac16 \cdot 5 \cdot i \cdot π \cdot 9}
|
-22,266 |
\left(1 + a\right) \cdot (a + 8 \cdot (-1)) = 8 \cdot (-1) + a^2 - 7 \cdot a
|
15,680 |
\sin^p(\|z\|)/\|z\| = \|z\|^{p + \left(-1\right)} \cdot \frac{1}{\|z\|^p} \cdot \sin^p(\|z\|)
|
4,855 |
(x + 1)^2 \cdot \left(x + 1\right) = x^3 + 3 \cdot x^2 + 3 \cdot x + 1 < x \cdot x \cdot x + x^3 + x^3
|
4,114 |
((B + C)^2 - B \cdot C \cdot 2)^2 - 2 \cdot B^2 \cdot C^2 = B^4 + C^4
|
46,519 |
\left(a_n = \sqrt{a_{n + \left(-1\right)} \cdot a_{1 + n}}\Longrightarrow a_n^2 = a_{n + 1} \cdot a_{n + (-1)}\right)\Longrightarrow \frac{a_n}{a_{n + (-1)}} = a_{1 + n}/(a_n)
|
-7,995 |
\tfrac{(-20 \cdot i - 30) \cdot (1 - 5 \cdot i)}{(1 - i \cdot 5) \cdot \left(5 \cdot i + 1\right)} = \frac{1}{-(i \cdot 5)^2 + 1^2} \cdot (-20 \cdot i - 30) \cdot (-5 \cdot i + 1)
|
-10,401 |
\dfrac{3}{h^2\cdot 20}\cdot 2/2 = \frac{6}{h^2\cdot 40}
|
17,846 |
(x^2)^{1/2} = ((-x) \cdot (-x))^{1/2} = |x|
|
34,364 |
0 > 1 + x rightarrow x \lt -1
|
21,509 |
-\frac12*\pi = ((-1)*\pi)/2
|
21,960 |
\tfrac12(3(-1) + 3^{m + (-1)}) + 1 = (3^{m + (-1)} + (-1))/2
|
5,883 |
r*(x_1 + x_2) = r*x_1 + r*x_2
|
37,797 |
z_1 + z_2 = z_2 - z_1 + 2\cdot z_1
|
35,849 |
(n^2 + n + 1) \cdot (n^3 - n + 1) = 1 + n^5 + n^4
|
39,265 |
\cos{i\cdot y} = (e^{-y} + e^y)/2 = \cosh{y}
|
-22,905 |
\frac{8*5}{5*5} = 40/25
|
17,886 |
1/(f_1 f_2) = \frac{1}{f_2 f_1}
|
-4,278 |
\frac{a^4}{a^3} \cdot 44/132 = \frac{a^4 \cdot 44}{a^3 \cdot 132}
|
-18,372 |
\dfrac{7 + y^2 + 8 \cdot y}{y^2 + y \cdot 7} = \dfrac{1}{y \cdot (y + 7)} \cdot (y + 1) \cdot (y + 7)
|
23,330 |
\binom{x}{m} = \frac{1}{m! (x - m)!} x!
|
20,602 |
e^{\frac43 \times \pi \times i} = (e^{\pi \times i \times 2/3})^2
|
-4,693 |
\dfrac{1}{y^2 + y\cdot 2 + 15\cdot (-1)}\cdot (y\cdot 2 + 2) = \frac{1}{3\cdot (-1) + y} + \dfrac{1}{5 + y}
|
-9,185 |
72 z + 16 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 z + 2 \cdot 2 \cdot 2 \cdot 2
|
34,435 |
8881 = 9025 + 144\times \left(-1\right)
|
4,818 |
x - d + a - b = a + x - b + d
|
11,919 |
\left(\left(z/2 = z\cdot 2 + 2(-1)\Longrightarrow z = z\cdot 4 + 4(-1)\right)\Longrightarrow 3z = 4\right)\Longrightarrow \frac43 = z
|
10,158 |
(x^2 + y^2) * (x^2 + y^2) = x^4 + x * x*y^2 + y^4 + x * x*y^2 = x^2 + x^2*y^2
|
-6,142 |
\tfrac{4}{z \cdot z + z\cdot 13 + 36} = \frac{1}{(9 + z) \left(z + 4\right)}4
|
-10,433 |
-\frac{1}{s\cdot 4}\cdot \left(s\cdot 4 + \left(-1\right)\right)\cdot 20/20 = -\frac{1}{80\cdot s}\cdot (80\cdot s + 20\cdot (-1))
|
17,271 |
0 = q^{j + (-1)}*b*b = q^{j + (-1)}*b^2 = q^{j + 2*\left(-1\right)}*b*q*b
|
14,437 |
\sum_{i=1}^x b_i + c\sum_{i=1}^x a_i = \sum_{i=1}^x (a_i c + b_i)
|
18,564 |
\dfrac{1}{7}\cdot 4 = 1 - \dfrac27 - 1/7
|
-20,541 |
6/6 \cdot (-10 \cdot t + 4)/(-8) = \left(-60 \cdot t + 24\right)/(-48)
|
32,094 |
2^0 \times 747 = 747
|
5,788 |
1995*d + 1995^2 = 1995*(1995 + d)
|
10,547 |
z^3-z^{-3}=(z-z^{-1})(z^2+1+z^{-2})
|
8,623 |
(y + 2(-1)) (y + 4) = y^2 + 2y + 8(-1)
|
-23,224 |
1 - 2/3 = \frac{1}{3}
|
5,923 |
\tfrac{2}{1 + x^2} \cdot x^2 = 2 - \frac{2}{x^2 + 1}
|
24,688 |
2 = |z| = |z + 4 (-1) + 4| \leq |z + 4 (-1)| + 4
|
4,767 |
4 \cdot (-1) + x = 1 \Rightarrow x = 5
|
24,602 |
(\dfrac12)^2 + (\frac{1}{2}) * (\frac{1}{2}) = 1/2
|
25,383 |
( A \times Y, B \times Y) = (B \times Y)^T \times A \times Y = Y^T \times B^T \times A \times Y = Y^T \times B^T \times A \times Y
|
-16,012 |
5/10 = -7 \cdot \frac{5}{10} + 8 \cdot \tfrac{5}{10}
|
5,966 |
(1 - z)\cdot \left(1 + z + z^2\right) = -z^3 + 1
|
31,549 |
z^3 + z^2 - z*10 + 8 = (z + 4)*(z + 2*(-1))*(z + (-1))
|
-3,485 |
\dfrac{1}{100}\cdot 4 = 0.04
|
3,348 |
3 + \frac19 = 3.111 \cdot \dotsm \approx \pi
|
-20,096 |
\frac{7}{a\cdot 7 + 42\cdot (-1)} = \frac{7\cdot 1/7}{a + 6\cdot (-1)}
|
16,432 |
d_2 \cdot d_2 + d_1^2 = 0 \Rightarrow d_1^2 = -d_2^2
|
29,749 |
Y' \cdot T + X' \cdot Y' + X \cdot T = X \cdot Y' \cdot T + X' \cdot Y' \cdot T + X' \cdot Y' + X \cdot T = X' \cdot Y' + X \cdot T
|
-26,425 |
\dfrac{1}{z^k}z^l = z^{-k + l}
|
29,154 |
i^2 = i^6 = i^{10}\cdot \dotsm\cdot i^{38}
|
23,070 |
9^k + 4^{k + 1} = \left(5 + 4\right)^k + 4^{k + 1} = 5\cdot b + 4^k + 4^{k + 1} = 5\cdot b + 5\cdot 4^k
|
-5,488 |
\frac{2 \cdot t}{(t + (-1)) \cdot (4 \cdot (-1) + t)} \cdot 1 = \frac{2 \cdot t}{t^2 - 5 \cdot t + 4}
|
1,531 |
0.35^3\cdot 0.65 = 0.35^3\cdot 0.65\cdot (0.35 + 0.65)^7
|
-8,015 |
(-4 - i\cdot 4)/(-2) = -\frac{1}{-2}\cdot 4 - 4\cdot i/(-2)
|
-4,411 |
\frac{5 + 3 \cdot z}{12 \cdot (-1) + z \cdot z + z} = \dfrac{2}{z + 3 \cdot (-1)} + \frac{1}{z + 4}
|
-25,276 |
4/3 \times 27^{\frac{1}{3}} = 4/3 \times 3 = 4
|
-19,036 |
\frac{7}{15} = \frac{D_s}{9 \cdot π} \cdot 9 \cdot π = D_s
|
5,203 |
\frac{1}{3!\cdot 2!\cdot 1!}\cdot 6! = \frac42\cdot 6\cdot 5 = 60
|
-13,001 |
26 + 11 (-1) = 15
|
-4,266 |
\frac15\times k\times 2 = 2/5\times k
|
7,978 |
4/10*5/11 = \frac{1}{11} 2
|
45,626 |
\cos^2{z} = \cos^2{z}
|
30,592 |
(x + (-1))^2 + 4\cdot x = (x + 1)^2
|
43,914 |
2 = 6 - (10 - 6)
|
4,639 |
(\sqrt{13} + 3)/16 = (1 + \left((-1) + \sqrt{13}\right)/4)/4
|
9,340 |
\left((\frac{1}{2^{1 / 2}}) \cdot (\frac{1}{2^{1 / 2}}) + (\frac{1}{2^{\frac{1}{2}}})^2\right)^{\frac{1}{2}} = (1/2 + \frac{1}{2})^{1 / 2} = 1
|
126 |
\sin{\theta}/(2*\sin{\frac{1}{2}*\theta}) = \cos{\frac{\theta}{2}}
|
-562 |
e^{\frac{i*\pi}{3}*1*3} = (e^{\frac{i}{3}*\pi})^3
|
-2,736 |
\sqrt{6}\cdot 4 + \sqrt{6} = \sqrt{6} + \sqrt{16} \sqrt{6}
|
19,106 |
( E*B*e, d) = ( B*e, E*d) = ( e, B*E*d)
|
27,266 |
q*q*x = q^2*x
|
6,517 |
\left\{C,B\right\}\Longrightarrow B = \{\overline{C},\overline{B}\}
|
38,092 |
z \in A \Rightarrow z \in A
|
11,334 |
\frac{\text{d}}{\text{d}x} \tan{x} = \sec^2{x} = 1 + \tan^2{x}
|
1,095 |
2 \times a - a + 1 = 2 \times a - a + (-1) = a + (-1)
|
8,741 |
9000 - 9^4 = 9000 + 6561\times (-1) = 2439
|
16,849 |
\int \frac{1}{1 + y^2} \cdot (1 + y^4 + \left(-1\right))\,\mathrm{d}y = \int \dfrac{y^4}{y \cdot y + 1}\,\mathrm{d}y
|
-6,392 |
\dfrac{1}{(j + 6)\times (j + 9)}\times j = \frac{1}{54 + j^2 + 15\times j}\times j
|
-10,782 |
-15 = 5 \cdot m + 30 + 6 = 5 \cdot m + 36
|
-8,065 |
\frac{45 \cdot i + 5}{5 - 5 \cdot i} \cdot \frac{5 + i \cdot 5}{5 \cdot i + 5} = \frac{5 + 45 \cdot i}{5 - 5 \cdot i}
|
10,279 |
(u + w)*(-w + u) = u * u - w^2
|
1,711 |
\dfrac{5}{5 + 4}\cdot \frac{6}{6 + 3} = 30/81 \approx 0.37
|
11,513 |
\frac{\mathrm{d}}{\mathrm{d}x} \tan^{-1}(x) = \dfrac{1}{\sec^2(\tan^{-1}(x))}
|
29,730 |
u \cdot ( \dfrac{1}{2}, \dfrac12) = 0 = u \cdot \left( 1/2, \tfrac{1}{2}\right)
|
-5,393 |
\frac{1}{10^6}\cdot 28.0 = \dfrac{28}{10^6}
|
272 |
9! - 2! \cdot 8! \cdot 3 + 3 \cdot 2! \cdot 7! = 151200
|
-4,416 |
(z + 5) \left(z + (-1)\right) = z^2 + 4z + 5(-1)
|
6,143 |
g \cdot g \cdot g - c^3 = (-c + g) \cdot (g^2 + g \cdot c + c^2)
|
-2,328 |
10/18 - 4/18 = 6/18
|
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