id
int64 -30,985
55.9k
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437k
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|---|---|
-22,764 |
\frac{5 \cdot 4}{5 \cdot 9} = 20/45
|
9,350 |
\dfrac{1}{2*2} = \frac{1}{2} * \frac{1}{2} = \frac{1}{4}
|
-8,856 |
80\cdot \pi = \pi\cdot 16 + 16\cdot \pi + \pi\cdot 48
|
7,471 |
7 = 3 \cdot (-1) + \frac{5 \cdot 3 \cdot 4}{1 \cdot 2 \cdot 3}
|
17,408 |
\cot(-\tfrac{\pi}{7} + \pi/2) = \cot{\frac{5*\pi}{14}}
|
31,417 |
3 = \frac{(1 + 2)!}{2! \cdot 1!}
|
22,014 |
\cos(X_2 + X_1) = \cos{X_1}\cdot \cos{X_2} - \sin{X_1}\cdot \sin{X_2}
|
-22,772 |
54/90 = \frac{54}{5*18}1
|
27,696 |
(x + 1)^2 = \sum_{k=1}^{x + 1} k + \sum_{k=1}^x k = 2\sum_{k=1}^x k + x + 1
|
20,577 |
(\left(-1\right) \cdot g)/11 = -\frac{g}{11}
|
-15,697 |
\frac{\frac{1}{x^3} n^4}{x^9 \frac{1}{n^3}}1 = \frac{1}{\frac{x^3}{n^4} \dfrac{1}{n \cdot n^2 \frac{1}{x^9}}}
|
20,039 |
(P - E) \left(E + P\right) = P^2 - E^2
|
32,212 |
\pi \cdot \frac{1}{4}/(\frac{1}{\pi}) = \frac{\pi^2}{4}
|
5,306 |
r + 1 = 0 \implies -1 = r
|
-22,831 |
72/16 = 8\cdot 9/(2\cdot 8)
|
-18,457 |
3\cdot g + 10\cdot (-1) = 9\cdot (g + 5\cdot (-1)) = 9\cdot g + 45\cdot (-1)
|
45,432 |
2*9 = 9 + 1 + 0 + 8
|
4,480 |
e^x\cdot 6 + C = y\cdot (x + 3\cdot (-1)) \Rightarrow \frac{C + 6\cdot e^x}{x + 3\cdot (-1)} = y
|
6,870 |
\frac{1}{((-1) + x)!}\cdot (Z - x + x + (-1))! = \frac{(Z + \left(-1\right))!}{(x + (-1))!}
|
27,351 |
9 = -1 + 10 = -1 + 10^{\frac{1}{2}} \cdot 10^{\frac{1}{2}} = (1 + 10^{1 / 2})\cdot (-1 + 10^{\frac{1}{2}})
|
-17,015 |
-6 = -6\left(-z\right) - 24 = 6z - 24 = 6z + 24 \left(-1\right)
|
29,630 |
(B + A) (-A + B) = B * B - A * A
|
36,741 |
-\frac{1}{2} + 1 = -1/2 + 1
|
33,589 |
(b + f) (x + 1) = \left(1 + x\right) f + b*(x + 1)
|
7,212 |
e^{1 + |x_2 - x_1|} = e^{|-x_1 + x_2|} e^1
|
36,799 |
-\frac{4}{4} + 4 \cdot \left(4 + 4\right) + 4 = 35
|
5,935 |
z \cdot z \cdot z \cdot y^3 = (z \cdot y)^3
|
-11,977 |
26/45 = p/(18 \pi)\cdot 18 \pi = p
|
21,557 |
6 + \left(3 + x + d\right)/9 = (d + 57 + x)/9
|
-4,774 |
\frac{-6\times z + 8\times (-1)}{z^2 + 4\times (-1)} = -\dfrac{5}{z + 2\times (-1)} - \frac{1}{z + 2}
|
22,923 |
(10^x + \left(-1\right)) \cdot t = 10^x \cdot t - t
|
-2,051 |
\pi \cdot \frac{1}{12} \cdot 5 + \pi \cdot 5/6 = \dfrac54 \cdot \pi
|
20,935 |
5*(\left(-1\right) + a) + 25 = 153 \Rightarrow 5*((-1) + a) = 128
|
-20,828 |
\frac{-6\cdot q + 24\cdot (-1)}{56\cdot \left(-1\right) - q\cdot 14} = \frac{3}{7}\cdot \frac{1}{8\cdot (-1) - 2\cdot q}\cdot (-2\cdot q + 8\cdot \left(-1\right))
|
13,841 |
\cosh\left(t\right) = \dfrac{1}{2} \cdot (e^t + e^{-t}) = \cos\left(i \cdot t\right)
|
126 |
\cos(\frac{x}{2}) = \sin\left(x\right)/(2\cdot \sin\left(x/2\right))
|
955 |
\frac{\frac17}{1/3\cdot \frac14} = 12/7
|
-6,090 |
\frac{2}{2\cdot k + 12\cdot \left(-1\right)} = \frac{2}{2\cdot \left(6\cdot (-1) + k\right)}
|
-11,774 |
16/49 = \left(\frac{4}{7}\right) \cdot \left(\frac{4}{7}\right)
|
11,879 |
(x + 3)^{1/2} = (x + 2)^2 + (-1) = (x + 3)^2 - 2\cdot (x + 3)
|
6,468 |
\frac{\text{d}}{\text{d}t} e^Y = Ye^Y = e^Y Y
|
4,159 |
-\left(n + (-1)\right)^2 = -n^2 + 4 n - 2 n + (-1)
|
-20,384 |
4/4*\frac{(-1)*r}{-r*5 + 4*(-1)} = \dfrac{1}{-20*r + 16*(-1)}*(r*(-4))
|
-25,050 |
\frac39\cdot 2/8 = \frac{6}{72} = \frac{1}{12}
|
-26,620 |
-z^2 + 6 \cdot 6 = \left(6 - z\right)\cdot (z + 6)
|
-2,428 |
(1 + 5)*\sqrt{13} = 6*\sqrt{13}
|
-18,710 |
0.3811 = \left(-1\right) \cdot 0.3446 + 0.7257
|
210 |
\sqrt{x \cdot x - 2\cdot x\cdot y + y^2} = \sqrt{(x - y)^2} = |x - y|
|
-5,768 |
\frac{2y}{y^2 + y*14 + 45} = \frac{2y}{(y + 5) (9 + y)}
|
-7,987 |
\frac{18 - i*4}{-3 - 5*i}*\frac{1}{-3 + i*5}*(5*i - 3) = \frac{1}{-5*i - 3}*(-4*i + 18)
|
910 |
(1 + \cos\left(q*2\right))/2 = \cos^2(q)
|
-22,128 |
\frac17 \cdot 6 = \frac{30}{35}
|
31,739 |
n \cdot 2 = -\left(\sqrt{-n \cdot 2}\right)^2
|
28,562 |
g \cdot l \cdot (D \cup X) = D \cup X = g \cdot l \cdot D \cup g \cdot l \cdot X
|
-3,918 |
\frac{t^5}{t^2}*66/24 = \frac{t^5*66}{24 t^2}
|
17,091 |
\tan(270 + 2 \cdot \theta) = \tan(90 \cdot 4 - -2 \cdot \theta + 90)
|
24,746 |
d_1 + d_2 + c = d_1 + d_2 + c
|
-19,587 |
7/4 \cdot 5/9 = \frac{1/4 \cdot 7}{9 \cdot \frac{1}{5}}
|
-6,558 |
\frac{4 c}{81 + c^2 - 18 c} = \frac{c*4}{(9 (-1) + c) (9 (-1) + c)}
|
-20,363 |
4/7*\frac{q + 9}{9 + q} = \frac{q*4 + 36}{63 + q*7}
|
33,138 |
Y_j\cdot Y_x = Y_j\cdot Y_x
|
35,357 |
\mathbb{E}\left[\dfrac1X\right] = \mathbb{E}\left[X\right]^{-1}
|
8,323 |
-77*43 + 23*144 = 1
|
17,599 |
B^3 + 1 = \left(B + 1\right) \cdot (1 + B^2 - B)
|
27,021 |
\pi^{1/2}/2 = \int_0^\infty e^{y^2}\,dy \gt \int_0^1 e^{y^2}\,dy
|
5,563 |
2(3(-1) + l) + l = 3l + 6(-1)
|
27,093 |
F \cdot x \cdot y = y \cdot x \cdot F
|
17,628 |
\frac{H_n}{H_{1 + 2 \cdot n} - H_n/2} = \frac{1}{-1/2 + H_{2 \cdot n + 1}/(H_n)}
|
3,299 |
\tfrac{3}{4} = -\dfrac{1}{4} + 1
|
47,072 |
2^9*3*11*31 = 523776
|
-14,030 |
\frac{1}{6 + 2}\cdot 56 = 56/8 = 56/8 = 7
|
-17,743 |
32 \cdot (-1) + 55 = 23
|
-9,295 |
3*3*3*3 p - 2*3*3 = 81 p + 18 \left(-1\right)
|
11,423 |
\tan(\tan^{-1}(x) + \tan^{-1}(x^3)) = \dfrac{1}{1 - x^4}\cdot (x + x^3) = \frac{1}{1 - x^2}\cdot x
|
9,922 |
(z - a) \cdot \left(z - b\right) = z^2 - (a + b) \cdot z + a \cdot b
|
-8,269 |
(-5)\cdot (-9) = 45
|
-19,473 |
\frac{\frac17\cdot 8}{3} = 1/(3\cdot \frac{7}{8})
|
-26,554 |
10^2 - \left(3\cdot y\right)^2 = (10 + 3\cdot y)\cdot (10 - 3\cdot y)
|
16,284 |
\binom{4}{3} \cdot \binom{(-1) + 0 + 4}{0} = 4
|
-26,617 |
28 - x * x*7 = 7*(-x * x + 4)
|
23,810 |
\tanh\left(x\right) = \sinh(x)/\cosh(x) = \frac{1}{1 + e^{-2 \cdot x}} \cdot \left(1 - e^{-2 \cdot x}\right)
|
18,704 |
-2 \cdot (i + 1) = (-2) \cdot (-1) - 2 \cdot (i + 2)
|
-952 |
\frac{1}{1} 2 = 2
|
-7,425 |
\frac16*4*\frac{3}{5}*2/4 = 1/5
|
6,210 |
\sin(\alpha + \tfrac14*\pi) = \cos{\frac{\pi}{4}}*\sin{\alpha} + \sin{\tfrac{1}{4}*\pi}*\cos{\alpha}
|
-20,621 |
\frac{1}{-K \cdot 70 + 21 \cdot (-1)} \cdot (K \cdot (-7)) = \frac{1}{3 \cdot (-1) - 10 \cdot K} \cdot (K \cdot (-1)) \cdot \dfrac{1}{7} \cdot 7
|
41,212 |
\frac{1}{2^{50}}*100! = 82890330549595738924128375352277498403022775854137923684377543671801902285904897746019649652421639883795821220526555136000000000000000000000000
|
6,519 |
|f|/|x| = |\dfrac{f}{x}|
|
21,439 |
E((-E(A) + A) \cdot (-E(A) + A)) = E(A^2) - E(A)^2
|
46,744 |
2\times 17^1 + 1 = 35 = 5\times 7
|
23,186 |
\frac{1}{-x + f} = -\frac{1}{x - f}
|
1,050 |
\frac45 \cdot y + \frac{1}{4} \cdot y = \dfrac{21}{20} \cdot y
|
16,164 |
A\times f = f\times A
|
-26,627 |
16 \cdot x^6 + 81 \cdot (-1) = -9^2 + \left(4 \cdot x^3\right)^2
|
321 |
3 + 2*\sqrt{2} + 3 - 2*\sqrt{2} = 6
|
20,288 |
7^{369}/350 = 7^{368}/50
|
32,672 |
h^{f + g} = h^f*h^g
|
21,793 |
\alpha_n+\beta_n=\beta_n+\alpha_n
|
22,676 |
\cos(z^3) + (-1) = 1 + (-1) - z^6/2 + \dots = \frac{1}{2} \cdot ((-1) \cdot z^6) + \dots
|
20,695 |
\frac{1}{x^2} \times k \times k = \left(k/x\right)^2
|
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