id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
21,391 |
\dfrac{2x}{x^2 + 1}1 = \frac{2x}{(x + i) (x - i)} = (x + i)^{-1} + (x - i)^{-1}
|
11,682 |
-T_0*y_0 + y*T = T*y - T_0*y + y*T_0 - y_0*T_0
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23,323 |
2^{1/3} = 2^{1/3} = (2^2)^{1/6}
|
26,043 |
Z\cdot B\cdot 2 = Z\cdot B + B\cdot Z
|
-20,821 |
\frac{1}{3\cdot t + 10\cdot (-1)}\cdot (5 + t)\cdot 7/7 = \dfrac{t\cdot 7 + 35}{21\cdot t + 70\cdot (-1)}
|
1,114 |
2\cdot 5 + 2\cdot 3 + 2\cdot 4 = 2\cdot (5 + 3 + 4)
|
27,053 |
\frac{29}{256} = \dfrac{1}{2048}(165 + 55 + 11 + 1)
|
34,605 |
(z + 1) \left(z^2 + 1\right) = z * z^2 + z^2 + z + 1
|
7,315 |
\pi \times 5/9 = \frac{10}{18} \times \pi
|
-4,539 |
(x + 4*\left(-1\right))*(3 + x) = x^2 - x + 12*\left(-1\right)
|
10,128 |
-3 = (a + b \cdot i) \cdot (a + b \cdot i) = a^2 + 2 \cdot a \cdot b \cdot i + b^2
|
-4,914 |
\frac{1}{100} \cdot 36.5 = \tfrac{36.5}{100}
|
-9,430 |
8y + 8y^2 = yy\cdot 2\cdot 2\cdot 2 + 2\cdot 2\cdot 2 y
|
-17,667 |
9(-1) + 10 = 1
|
3,702 |
15 = \frac{1}{5} \cdot (3 \cdot (-1) + 78)
|
13,571 |
\sin(b + d) = \cos{b}*\sin{d} + \sin{b}*\cos{d}
|
-3,052 |
10\times \sqrt{10} = \sqrt{10}\times (1 + 4 + 5)
|
554 |
y*x - x*z + y*z = (-y + x)*(y - z) + y^2
|
3,127 |
\sqrt{x^2 + x\cdot 2} = \sqrt{(-1) + (1 + x)^2}
|
-30,561 |
96/48 = \dfrac{48}{24} = \frac{1}{12}\cdot 24 = 2
|
37,232 |
\left|{B*C*A + I}\right| = \left|{I + A*C*B}\right|
|
-21,092 |
\frac{1}{10}*1 = \frac{10}{100}
|
31,517 |
\tfrac{6}{720} = \frac{1}{120}
|
8,604 |
x \cdot x + 3 \cdot x + 2 \cdot (-1) = \frac{1}{x + 1} \cdot (x^3 + 4 \cdot x^2 + x + 2 \cdot \left(-1\right))
|
-28,511 |
x^2 + 8 x + 52 = x x + 8 x + 16 + 36 = \left(x + 4\right)^2 + 36 = (x + 4) (x + 4) + 6^2
|
-19,042 |
29/30 = \frac{1}{25 \cdot \pi} \cdot A_r \cdot 25 \cdot \pi = A_r
|
-17,405 |
1.023 = \frac{1}{100} \cdot 102.3
|
33,891 |
0 = \frac{1}{y^2 - x}\cdot (y - x^2) \Rightarrow x^2 = y
|
25,503 |
\sinh\left(2\right) = \frac{e^4 + (-1)}{2\times e \times e} \approx 243/67
|
14,718 |
-12 a + 144 < 0 \Rightarrow 12 < a
|
21,422 |
2 = (x + i) \cdot (x + i) = x^2 + 2\cdot i\cdot x + (-1)
|
1,526 |
\frac{4}{2*l} = -2*l = -2*e^{\frac{l*\pi}{2}} = 2*e^{((-1)*l*\pi)/2}
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-22,287 |
(k + 9) \left(5 + k\right) = k^2 + k\cdot 14 + 45
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16,885 |
\tfrac{3}{5}\cdot \dfrac47\cdot \tfrac{1}{3}\cdot 2 = \dfrac{8}{35}
|
10,398 |
h^{x + d} = h^x\cdot h^d
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9,405 |
\frac62\cdot (2 + 1) = \frac{1}{2}6\cdot 3 = 6/6 = 1
|
-22,366 |
l^2 - 3 \cdot l + 18 \cdot (-1) = (3 + l) \cdot (l + 6 \cdot (-1))
|
33,903 |
|x - y| = |1| |x - y|
|
15,791 |
\operatorname{E}[\sum_{x=1}^n X_x] = \operatorname{E}[\sum_{x=1}^n X_x]
|
20,062 |
\frac1z \cdot 2 \cdot 1/2 = 1/z
|
4,848 |
\left(bx\right)^2 = \left(bx\right)^2
|
17,595 |
1 = (h + g)\cdot (x + e) = h\cdot x + g\cdot x + h\cdot e + g\cdot e
|
4,236 |
(f + g) \cdot (f - g) = f \cdot f - g^2
|
26,213 |
37\cdot 100\cdot 1^2 + 20 = 6\cdot 20 + 6^2\cdot 100
|
35,696 |
y \cdot y \cdot y + (-1) = (y + (-1)) \cdot (y^2 + y + 1)
|
-6,016 |
\frac{3}{(t + 10)*(4*(-1) + t)}*t*\tfrac{15}{15} = \tfrac{t*45}{(t + 10)*(t + 4*(-1))*15}
|
32,442 |
2^y = 3^y \Rightarrow y = 0
|
242 |
\frac{1}{2}(-\frac{1}{2} + 1) = (1/2)^2
|
-10,150 |
1^{-1} = \frac55
|
25,007 |
Cv = Cv
|
-26,537 |
a^2 - b^2 = (-b + a) \cdot (a + b)
|
6,515 |
\dfrac{z}{-z^6\cdot 1/2} = -\frac{2}{z^5}
|
-5,029 |
5.32\cdot 10 = \frac{10}{1000}\cdot 5.32 = 5.32/100
|
16,810 |
|x + y|^2 = \left(x + y\right)^2 = x * x + 2xy + y^2
|
10,663 |
a\times 3 = a\times 2 + a
|
16,580 |
y/15\cdot 2 = \dfrac{2y}{15}1
|
819 |
U = 2\times U - U
|
14,283 |
(x - T)\cdot (T + x) = x^2 - T^2
|
446 |
\sin(c + f) = \cos\left(f\right) \cdot \sin(c) + \sin(f) \cdot \cos(c)
|
27,041 |
\left(g + f\right)^2 - g\cdot f\cdot 2 = f^2 + g^2
|
48,774 |
\tan^2(x) = 3\Longrightarrow \cos(2 \cdot x) = \frac{1 - \tan^2\left(x\right)}{1 + \tan^2(x)} = -\frac12 = \cos(2 \cdot \pi/3)
|
26,444 |
2^x - 2^{x + (-1)} = 2^{x + \left(-1\right)}\cdot (2 + (-1)) = 2^{x + (-1)}\cdot (\dotsm!)!
|
880 |
(c + x)^2 = c^2 + 2\cdot c\cdot x + x^2 \leq 2\cdot (c^2 + x \cdot x)
|
12,031 |
\sin^n(x) = \sin^2\left(x\right)*\sin^{2*(-1) + n}(x)
|
18,539 |
5.8 = (-1) + 0.3\cdot 10 + 0.6\cdot 6 + 0.1\cdot 2
|
1,522 |
\left(x - z\right) (x^{n + (-1)} + x^{n + 2\left(-1\right)} z + \dotsm + z^{n + 2(-1)} x + z^{\left(-1\right) + n}) = x^n - z^n
|
40,522 |
-a = a*(-1)
|
3,683 |
\dfrac{1}{h\cdot k} = \frac{1}{k\cdot h} = \frac{\frac1k\cdot k/h}{k}
|
21,784 |
\dfrac{2}{2^2} = \frac12
|
12,575 |
-0 \cdot 0 + (\operatorname{re}{(y)})^2 = \operatorname{re}{\left(y\right)}\Longrightarrow \frac{1}{2}\cdot (1 \pm 1) = \operatorname{re}{(y)}
|
5,943 |
\frac16\left(8^3 + 10^3 - 9^3*2\right) = 9
|
28,469 |
2^m = -2^m + 2^{1 + m}
|
27,251 |
3 = \frac{1}{-2 + 3} \cdot (2 \cdot (-1) + 5)
|
16,377 |
(2 + m)^2 - m^2 = 4 + 4\cdot m
|
32,588 |
5\cdot 5\cdot 8 = 13^2 + 2\cdot 13 + 5
|
26,007 |
Y \cap x = (Y \cap x)^g = x \cap Y^g
|
-1,304 |
7*1/6/(1/4*(-7)) = \frac{7}{6}*\left(-\dfrac47\right)
|
3,732 |
3*z^2*\varepsilon = z^2*\varepsilon + z^2*\varepsilon + \varepsilon*z^2
|
-3,699 |
k^5/k \cdot \frac{18}{20} = \frac{k^5}{k \cdot 20} \cdot 18
|
17,261 |
1/a = h \Rightarrow a = \frac{1}{h}
|
32,787 |
R_b R_a = R_a R_b
|
-8,085 |
\frac{-8i + 2}{3 + 5i} \tfrac{-i*5 + 3}{3 - i*5} = \frac{1}{3 + 5i}(2 - 8i)
|
7,293 |
n + t + \frac{19 t}{80} = n + 99 t/80 = 100 \Rightarrow n = \dfrac{1}{80}((-99) t) + 100
|
3,880 |
\frac12 \cdot \dfrac{1}{2} \cdot \dfrac12/2/2 = \frac{1}{32}
|
17,039 |
36 + 4\cdot x^2 - x\cdot 26 = (18\cdot (-1) + x\cdot 4)\cdot (2\cdot (-1) + x)
|
-29,627 |
x \cdot 6 + 8 \cdot x^2 \cdot x + 3 \cdot x \cdot x = \frac{\mathrm{d}}{\mathrm{d}x} (x^4 \cdot 2 + x^3 + x^2 \cdot 3)
|
1,785 |
(1 + E_1)/6 + \tfrac56*(H + 1) = H \Rightarrow H = E_1 + 6
|
-19,142 |
17/18 = \frac{A_x}{81 \cdot \pi} \cdot 81 \cdot \pi = A_x
|
24,042 |
\left(2^{1/9}\right)^2 * 2^{1/9} = 2^{1/3}
|
15,568 |
-i \cdot M \cdot x + i \cdot M \cdot x = i \cdot M \cdot x - i \cdot x \cdot M
|
16,706 |
\frac{1}{(1 - z)^2} = \frac{1}{(-z + 1)\cdot (-z + 1)}
|
25,825 |
\operatorname{E}((-\operatorname{E}(A) + A)^2) = \operatorname{E}(A^2) - \operatorname{E}(A)^2
|
32,147 |
1 + 2*n = 2*(1 + n) + (-1)
|
-11,540 |
4 + 6 \cdot i = 4 + 0 \cdot (-1) + i \cdot 6
|
-8,089 |
(2 - 16 \cdot i - 10 \cdot i + 80 \cdot (-1))/26 = \left(-78 - 26 \cdot i\right)/26 = -3 - i
|
26,926 |
\frac{b}{f^N} = b\cdot f^{-N}
|
17,262 |
k^4 = k^2\cdot k^2 > 6\cdot k^2
|
-18,470 |
-\frac{1}{8}\cdot 36 = -9/2
|
27,988 |
3\cdot n^2 - 3\cdot n + 1 = n^3 - ((-1) + n) \cdot ((-1) + n) \cdot ((-1) + n)
|
-20,426 |
\dfrac{5}{g + 5}*1/5 = \dfrac{1}{25 + 5*g}*5
|
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