id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
9,722 |
\cos(2\gamma_i) = \cos\left(\pi*2 - 2\gamma_i\right)
|
40,138 |
6 = 2*3 = (1 + (-5)^{\tfrac{1}{2}})*\left(1 - \left(-5\right)^{\dfrac{1}{2}}\right)
|
15,838 |
(z + 5)*(z + 7*(-1)) = z * z - 2*z + 35*(-1) = z^2 - 2*z + 1 + 36*(-1) = (z + (-1)) * (z + (-1)) + 36*(-1)
|
-22,274 |
16 + s^2 - 10 s = (s + 2\left(-1\right)) \left(s + 8\left(-1\right)\right)
|
16,871 |
\left(2^3 + 7\cdot 2^2 + 8\cdot (-1) \leq 0\Longrightarrow 8 + 28 + 8\cdot (-1) \leq 0\right)\Longrightarrow 28
|
39,671 |
1 = 1^2 - 0^2
|
25,001 |
\frac{1}{k} \cdot (k + 3 \cdot (-1)) = 1 - \frac{3}{k}
|
-14,023 |
\tfrac{1}{2 + 9}\cdot 11 = \tfrac{11}{11} = \dfrac{1}{11}\cdot 11 = 1
|
22,284 |
(3 (-1) + z) (6 (-1) + z) = z^2 - z*9 + 18
|
-23,090 |
-1/3 (-\dfrac{1}{9}) = 1/27
|
23,713 |
\sqrt{10} \cdot h + f \cdot 2 + \sqrt{6} \cdot b = 0 \Rightarrow 0 = f, 0 = b \cdot \sqrt{6} + h \cdot \sqrt{10}
|
-18,808 |
\dfrac{-20}{4} = -5
|
-3,414 |
(5 + 3 + 2)\cdot \sqrt{11} = 10\cdot \sqrt{11}
|
37,571 |
\infty \cdot \left(0 + (-1)\right) = \infty \cdot (-1) = -\infty
|
13,193 |
-\frac{1}{z + (-1)} + \frac{1}{2\cdot (-1) + z} = \frac{1}{\left(z + \left(-1\right)\right)\cdot (z + 2\cdot (-1))}
|
19,257 |
\frac{\mathrm{d}}{\mathrm{d}y} \left(ss^{1/2}\right) = \frac{s}{2s^{1/2}} + s^{1/2} = 3/2 s^{1/2}
|
-8,102 |
10 = 5*4/2
|
-8,088 |
(-3 - 7\cdot i + 3\cdot i + 7\cdot \left(-1\right))/2 = \left(-10 - 4\cdot i\right)/2 = -5 - 2\cdot i
|
27,110 |
\frac{1}{15} + 1/10 - \tfrac{1}{22} + 1/11 = 1/33
|
-10,493 |
\tfrac15\cdot 5\cdot \left(-\frac{q\cdot 4 + 5}{3\cdot q + (-1)}\right) = -\frac{1}{15\cdot q + 5\cdot (-1)}\cdot (20\cdot q + 25)
|
24,718 |
\frac{1}{4! \cdot 2!} \cdot 6! = {6 \choose 2}
|
664 |
(-1) + p = \frac{p + (-1)}{( p + (-1), k \times a)} \implies 1 = ( (-1) + p, a \times k)
|
14,348 |
2 \cdot l + 1 = 0 + 2 \cdot l + 1 = 2 + 2 \cdot l + (-1) = \dotsm = 2 \cdot l + 2 \cdot (-1) + 3 = 2 \cdot l + 1
|
24,006 |
-\dfrac82 = -4
|
-6,251 |
\dfrac{3}{2\cdot (x + 6\cdot (-1))} = \frac{3}{2\cdot x + 12\cdot \left(-1\right)}
|
23,977 |
\sin(-B + \pi/2) = \cos{B}
|
-26,654 |
(1 + z \cdot 3) \cdot (z + 7 \cdot (-1)) = 3 \cdot z^2 - 20 \cdot z + 7 \cdot (-1)
|
-11,616 |
-20 + 12\cdot \left(-1\right) + i\cdot 8 = 8\cdot i - 32
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-10,503 |
-\dfrac{27}{3 \cdot (-1) + x \cdot 6} = -\dfrac{9}{2 \cdot x + (-1)} \cdot 3/3
|
1,090 |
5.5 x = \frac{1}{10}(10 x + x + 2x + x*3 + x*4 + x*5 + x*6 + x*7 + x*8 + x*9)
|
-15,946 |
12/10 = 6*\frac{7}{10} - 10*\frac{1}{10}3
|
-15,571 |
\frac{1}{x^{25}\cdot (\frac{1}{n^5}\cdot x) \cdot (\frac{1}{n^5}\cdot x) \cdot (\frac{1}{n^5}\cdot x)} = \dfrac{1}{\frac{1}{n^{15}}\cdot x^3\cdot x^{25}}
|
26,957 |
\dfrac{1}{4}(14 + 2) \left(4 + 5(-1)\right) = 0 + 0 + G \implies -4 = G
|
26,904 |
11 = -((-1) + 2 + 2 + 2) + 8 + 4 + 4 + 4 + 2 \cdot \left(-1\right) + 2 \cdot (-1)
|
25,674 |
2/3\cdot 1/(3\cdot 3) = \frac{1}{27}\cdot 2
|
23,310 |
\sqrt{180^2 + 60^2} = 60*\sqrt{10}
|
22,287 |
y + 3 \left(-1\right) = -y - 1 \Rightarrow y = 1
|
632 |
z \cdot \frac{\mathrm{d}y}{\mathrm{d}t} + \frac{\mathrm{d}z}{\mathrm{d}t} \cdot y = \frac{\partial}{\partial t} (z \cdot y)
|
1,516 |
(y + 2)^{\frac{1}{2}} = \left(4 + y + 2 \cdot (-1)\right)^{\tfrac12} = 2 \cdot (1 + \left(y + 2 \cdot (-1)\right)/4)^{\frac12}
|
22,602 |
\left(g^3 + g^2\cdot x + g\cdot x^2 + x^3\right)\cdot (g - x) = -x^4 + g^4
|
25,732 |
z^4 + 5 \cdot z^2 + 4 = \left(z^2 + 1\right) \cdot \left(z^2 + 4\right)
|
9,356 |
\cos(x + \alpha) = \cos{\alpha} \times \cos{x} - \sin{x} \times \sin{\alpha}
|
-15,530 |
\dfrac{{(r^{3})^{3}}}{{(rn^{-3})^{-1}}} = \dfrac{{r^{9}}}{{r^{-1}n^{3}}}
|
5,759 |
u*u^Z*x = u*x*u^Z
|
24,080 |
\|x_t - x_{1 + t}\|^2 \leq 0\Longrightarrow x_t = x_{t + 1}
|
26,624 |
(-1) + 2 \cdot x = 2 \cdot \left(-1/2 + x\right)
|
5,701 |
x = a^2\cdot a \cdot a \cdot a\cdot x = a^2\cdot x\cdot a^3 = \frac{x\cdot a^6}{a}\cdot 1 = \dfrac{x\cdot a^6}{a}\cdot 1 = \dfrac{x\cdot a}{a}
|
39,506 |
-1 = ((-1)^{\frac{1}{2}})^2
|
22,558 |
\left(x + y\right)^2 = x^2 + x*y*2 + y^2
|
-1,923 |
\pi \cdot 19/12 + \pi \cdot \frac54 = \pi \cdot \frac16 \cdot 17
|
36,494 |
(-1) + \sec^2{\theta} = \tan^2{\theta}
|
5,065 |
(k + 1)^2 \cdot (k + 1) - k + 1 = k^3 + 3 \cdot k^2 + k \cdot 2
|
27,565 |
10/60*\frac{20}{60}*\frac{1}{60}*30 = \frac{1}{36}
|
-7,706 |
\frac{-5 - 25 \cdot i}{-i + 5} \cdot \frac{1}{5 + i} \cdot \left(i + 5\right) = \frac{1}{-i + 5} \cdot (-25 \cdot i - 5)
|
4,935 |
e^{1/x} = e^{\frac1x} = 1 + 1/x + \dots > 1 + \tfrac1x
|
-26,175 |
0.3*10 + \frac1510 = 3 + 2 = 5
|
13,546 |
A_4 = \left\{3, 1, 4\right\} rightarrow 3 = |A_4|
|
34,261 |
-\pi/3 = \arcsin(\sin{\dfrac{\pi*4}{3}})
|
-15,782 |
-53/10 = -7\cdot \frac{9}{10} + 10/10
|
-400 |
\pi \cdot 49/6 - 8\pi = \pi/6
|
25,562 |
|(x_1 - A + \cdots + x_n - A)/n| = |\left(x_1 + \cdots + x_n\right)/n - A|
|
18,793 |
43 = 3 \times 14 + 1
|
21,300 |
((-1) + g)\cdot (g + 1) = g \cdot g + (-1)
|
-9,231 |
2\cdot 2\cdot 2\cdot 5\cdot c\cdot c - 5\cdot c = c^2\cdot 40 - 5\cdot c
|
-11,478 |
-i\cdot 16 - 20 + 0\cdot (-1) = -20 - i\cdot 16
|
3,278 |
\frac{1 / 16}{2} \cdot 1 = 1/32
|
16,739 |
Y_1 Y_1 Y_2 = -Y_1 Y_2 Y_1 = Y_2 Y_1 Y_1
|
-5,320 |
1.3/10000 = \frac{1}{10000} \cdot 1.3
|
16,945 |
v = z^3 \implies \frac{\mathrm{d}v}{\mathrm{d}z} = z^2\cdot 3
|
38,375 |
det\left(A\right) = 0 rightarrow A
|
16,637 |
D*x = 1 \implies D = 1/x
|
-2,588 |
\sqrt{3}*6 = (4 + 5 + 3(-1)) \sqrt{3}
|
2,696 |
\frac{\mathrm{d}}{\mathrm{d}x} 1/y = -\frac{1}{y \cdot y} \cdot \frac{\mathrm{d}y}{\mathrm{d}x}
|
-29,561 |
\left(4\cdot x^3 - x^2 + 3\right)/x = \frac{3}{x} + \dfrac1x\cdot x^3\cdot 4 - \frac{x^2}{x}
|
-5,133 |
\tfrac{1}{1000}\cdot 66.6 = 66.6/1000
|
22,015 |
\frac17 = \frac{3}{7}\cdot 2/6
|
-708 |
(e^{11\cdot \pi\cdot i/12})^{17} = e^{\frac{11}{12}\cdot i\cdot \pi\cdot 17}
|
9,499 |
7 \cdot 1/36/(\dfrac14) = \frac79
|
-625 |
e^{7 \cdot \pi \cdot i/3} = \left(e^{i \cdot \pi/3}\right)^7
|
-18,374 |
\dfrac{x}{(3 + x) \cdot (x + 2 \cdot \left(-1\right))} \cdot (x + 3) = \frac{x^2 + x \cdot 3}{x^2 + x + 6 \cdot (-1)}
|
29,682 |
\left(-B + A\right) \cdot (B + A) = A^2 - B^2
|
-17,079 |
-5 = -5 \left(-4 l\right) - 10 = 20 l - 10 = 20 l + 10 (-1)
|
31,163 |
4 \cdot x^2 = (2 \cdot x)^2 = 2 \cdot 2 \cdot x^2
|
48,280 |
0 = \sin{-\pi}
|
5,783 |
-(M + (-1))^2 = -2\cdot M - M^2 + 4\cdot M + (-1)
|
1,157 |
d_1 + d_2 - \frac{d_1\cdot d_2}{d_1 + d_2} = \frac{1}{d_2 + d_1}\cdot \left(d_1^2 + d_2\cdot d_1 + d_2 \cdot d_2\right)
|
23,833 |
\frac{X}{X + Y} = \left(1 + \frac{-Y + X}{X + Y}\right)/2
|
-23,088 |
4/3\cdot (-\tfrac19\cdot 32) = -128/27
|
6,608 |
2 + 4 + 6 + \dots + 2\cdot k = k\cdot \tfrac{1}{2}\cdot (2\cdot k + 2) = k^2 + k
|
23,422 |
\sin{x} = \sin(1 + x + (-1)) = \sin{1} \cdot \cos\left(x + \left(-1\right)\right) + \sin(x + (-1)) \cdot \cos{1}
|
22,466 |
\dfrac{\dfrac{\pi*5}{3}*12^2}{2} = \pi*120
|
36,099 |
(7 \cdot 7 + \left(-3\right) \cdot \left(-3\right))^{1 / 2} = 58^{1 / 2}
|
13,229 |
480 = 4\cdot 5\cdot 4\cdot 2\cdot 3
|
42,630 |
16807 = 1527 \times 11 + 10
|
-9,747 |
0.01\cdot (-84) = -84/100 = -\frac{21}{25}
|
16,880 |
-x - d = -(x + d)
|
-18,420 |
\dfrac{m^2 + m}{7*\left(-1\right) + m^2 - 6*m} = \frac{m}{(m + 1)*(7*\left(-1\right) + m)}*\left(1 + m\right)
|
2,555 |
\frac{1}{2*3} = 1/2 - 1/3
|
-7,728 |
\frac15\cdot (5\cdot i - 5) = 5\cdot i/5 - 5/5
|
8,630 |
x\cdot 114/100\cdot \frac{86}{100} = x
|
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