id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
1,522 |
(x - z)*(x^{(-1) + l} + x^{l + 2*(-1)}*z + \cdots + z^{2*\left(-1\right) + l}*x + z^{(-1) + l}) = -z^l + x^l
|
-27,686 |
\frac{\text{d}}{\text{d}x} \left(18 \cdot \sin{x}\right) = \cos{x} \cdot 18
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13,278 |
0 = 2 + 4(-1) + x \Rightarrow 2 = x
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-1,303 |
5/1 \cdot (-9/7) = (1/7 \cdot (-9))/(\tfrac15)
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40,312 |
((-1) + z)\times (2 + z) = 2\times (-1) + z^2 + z
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10,179 |
\dfrac{1}{\frac{1}{5^l}*3^l} = (\frac53)^l
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-3,042 |
-\sqrt{8} + \sqrt{50} = \sqrt{25\cdot 2} - \sqrt{4\cdot 2}
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-7,008 |
\frac{6}{7}\cdot 3/8 = 9/28
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18,267 |
2\left( 3, 4\right) = [6,8] = \emptyset
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17,063 |
55 = \tfrac{11!}{9! \cdot 2!}
|
1,827 |
\left(l + 1\right) \cdot \left(l + 1\right)^2 + 2\cdot (l + 1) = l^3 + 3\cdot l^2 + 5\cdot l + 3 = l^2 \cdot l + 2\cdot l + 3\cdot \left(l^2 + l + 1\right)
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-1,885 |
\frac{1}{4}\cdot 7\cdot \pi + \pi/6 = \frac{23}{12}\cdot \pi
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-10,607 |
-\dfrac{1}{k^2\cdot 4}\cdot \left(k\cdot 20 + 8\right) = -\frac{2 + k\cdot 5}{k \cdot k}\cdot 4/4
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-8,099 |
45 = \dfrac{9*10}{2}
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-20,792 |
8/8 \cdot \frac{1}{-x \cdot 6 + 2} \cdot ((-5) \cdot x) = \dfrac{1}{-x \cdot 48 + 16} \cdot (\left(-40\right) \cdot x)
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13,647 |
x \cdot x^Z \cdot f = x \cdot f \cdot x^Z
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4,313 |
26\times 1/9/(13\times \frac19) = 2 = B \Rightarrow B = 2
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38,497 |
\frac{1}{1 + |y|} y = \frac{y}{1 + y} = 1 - \frac{1}{1 + y}
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-28,811 |
\tfrac12\cdot (0 + 10) = 10/2 = 5
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15,399 |
\frac{1}{\sec^4\left(x\right)} + 1 = 1 + \cos^4(x) = \frac{1}{8}*(4*\cos(2*x) + \cos(4*x) + 11)
|
7,914 |
1 + 2 + ... + l + (-1) + l - l = 1 + 2 + ... + l + \left(-1\right)
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-20,838 |
\frac{q + (-1)}{(-1) + q} \cdot (-\dfrac14) = \frac{1 - q}{4 \cdot (-1) + 4 \cdot q}
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-25,810 |
\frac{\frac{1}{9}}{4} \cdot 2 = 2/36
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13,565 |
1.0*10^{17} = 2.0*10^3*10^{13}*5
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16,475 |
\frac{1}{h_2^{h_1}} = h_2^{-h_1}
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-2,659 |
\sqrt{25} \cdot \sqrt{3} + \sqrt{3} \cdot \sqrt{4} = 5 \cdot \sqrt{3} + \sqrt{3} \cdot 2
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-22,668 |
-1/4\cdot \left(-4/5\right) = \left((-1)\cdot (-4)\right)/(4\cdot 5) = 4/20 = \frac15
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31,915 |
(x + (-1)) * (x + (-1)) = x^2 - 2*x + 1 \implies \left(x + (-1)\right)^2 + (-1) = -x*2 + x^2
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-4,972 |
10^0\times 0.56 = 0.56\times 10^{(-5)\times (-1) - 5}
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5,943 |
9 = (8^3 + 10^3 - 2\cdot 9 \cdot 9 \cdot 9)/6
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-27,485 |
g^3\cdot 22 = 2\cdot g\cdot g\cdot g\cdot 11
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18,152 |
120 - 3\cdot i > 0 \implies i < 40
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4,652 |
-\sqrt{a} + \sqrt{b} = \dfrac{-a + b}{\sqrt{a} + \sqrt{b}}
|
24,940 |
a^l \cdot b^n = a^l \cdot b^n
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9,691 |
\lim_{x \to -\infty} -x + x = x + \lim_{x \to -\infty} (x^2 + 5*x + 3)^{\dfrac{1}{2}}
|
1,108 |
\|Y\|*\|Y\| = \|Y\|^2
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6,389 |
9*n + 6*k = 3*3*n + 2*3*k = 3*(3*n + 2*k)
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-15,210 |
\frac{1}{\frac{1}{q^2} \cdot p} \cdot q^{20} = \frac{1}{\dfrac{1}{q^{20}} \cdot \frac{1}{1/p \cdot q^2}}
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-6,748 |
\frac{4}{100} + \frac{1}{100}\cdot 50 = 5/10 + 4/100
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11,957 |
\frac12(2 + n^2 - n \cdot 3) - n + 2(-1) + 2 = (3\left(-1\right) + n) (n + 2\left(-1\right))/2 + 2
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-30,262 |
\dfrac{x^2-12x+20}{x-10}=\dfrac{\cancel{(x-10)}(x-2)}{\cancel{x-10}} =x-2
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-30,898 |
-3\cdot 6 + 55 = 37
|
6,793 |
1/4 + 2*1/4 + \frac14*3 + 4*\frac{1}{4} = 2.5
|
-16,489 |
10 \sqrt{12} = \sqrt{4 \cdot 3} \cdot 10
|
-539 |
e^{14 \frac{5}{6}i\pi} = (e^{5i\pi/6})^{14}
|
26,206 |
x^2 + x + 2 \cdot \left(-1\right) = (2 + x) \cdot ((-1) + x)
|
16,630 |
\dfrac{1}{128}21 = 63/384
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22,985 |
2^{n + 1} - n^2 + 3\cdot \left(-1\right) = (1 + 1)^{1 + n} - n^2 + 3\cdot (-1)
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16,804 |
\frac{1}{12}7 = 1/4 + \frac13
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33,567 |
1 - \dfrac{1}{2\cdot n + 1}\cdot n = \frac{n + 1}{2\cdot n + 1}
|
12,918 |
2\cdot 3^2 = 18 = 34 + 16\cdot (-1)
|
34,938 |
det\left(It - xX\right) = det\left(It - xX\right)
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-19,817 |
0.01\cdot \left(-122\right) = -122/100 = -1.22
|
11,584 |
2 \cdot \pi \cdot 2 \cdot 16 = \pi \cdot 64
|
11,235 |
x + 7 = x - -7
|
32,033 |
xz = xz = z = 2 \neq 3 = 2x = zx = zx
|
27,805 |
(\frac{x}{2})! D * D*\left(O^{22}\right)^{x/2} = D * D*\left(O^{22}\right)^{x/2}*2*3\dotsm x/2
|
7,676 |
\int (1 + v) \sqrt{v}\,dv = \int \left(v^{1/2} + v^{\frac32}\right)\,dv
|
11,933 |
(2^l)^2 = 2^{l*2}
|
23,832 |
50 \cdot x + y \cdot 20 = 1020\Longrightarrow 102 = 5 \cdot x + y \cdot 2
|
30,839 |
2^{1/2} = \dfrac{2 - a/b}{\frac{a}{b} + (-1)} = \frac{1}{a - b} \cdot (2 \cdot b - a)
|
10,426 |
4 \cdot \left(-1\right) + 4 \cdot (1 + x^2) = 4 \cdot x^2
|
26,575 |
4/2 = \tfrac11 \cdot 2 = 6/3 = \cdots
|
31,709 |
\frac{1}{1! \cdot 2! \cdot 1! \cdot 1!} \cdot 5! = 60
|
-23,301 |
3/10 = \frac{3}{4}\cdot 2/5
|
32,046 |
4\cdot k = (k + 1)^2 - (k + (-1))^2
|
24,041 |
\sin(x) = \sin(x + 2\cdot \pi)
|
6,977 |
a = 2 \cdot a \cdot f' \cdot g - a \cdot a \cdot x\Longrightarrow x \cdot a = f' \cdot g \cdot 2 + (-1)
|
33,385 |
\cos^2{x} \cos^2{x} = \cos^4{x}
|
7,787 |
\frac{1}{\sqrt{k}} = \frac{2}{\sqrt{k} + \sqrt{k}} \lt \dfrac{2}{\sqrt{k} + \sqrt{k + (-1)}}
|
22,320 |
4 + x^2 + 2x = (x + 1) \cdot (x + 1) + 3
|
38,556 |
(e^x)^2 = e^{2\cdot x} \neq e^{x^2}
|
23,878 |
h_i\cdot h_i\cdot h_i = h_i \cdot h_i^2
|
-30,565 |
-\frac{1}{-81}\cdot 243 = -\frac{81}{-27} = -27/\left(-9\right) = 3
|
29,483 |
3\cdot x = \frac{x^3\cdot 3}{x^2}
|
23,031 |
\left(2 = \dfrac{1}{b^2} \cdot x^2\Longrightarrow 2 \cdot b^2 = x^2\right)\Longrightarrow 2^{1 / 2} \cdot b = x
|
29,612 |
c \cdot (4 + 4 + 4) = 6 \cdot 2\Longrightarrow c = 1
|
-2,889 |
11^{1 / 2} \times 3 = (5 + 2 \times (-1)) \times 11^{\frac{1}{2}}
|
-20,973 |
\frac{1}{-t\cdot 21 + 12}\cdot (16 - 28\cdot t) = \frac{-t\cdot 7 + 4}{-7\cdot t + 4}\cdot \frac43
|
-7,031 |
5/13*\frac{6}{14} = \frac{1}{91}*15
|
9,711 |
2^4*5*3 * 3 = 720
|
11,844 |
x^2 + z^2 = 10^2 rightarrow z = \sqrt{10^2 - x^2}
|
-3,356 |
11^{1 / 2} \cdot 16^{\frac{1}{2}} - 11^{\dfrac{1}{2}} = -11^{\dfrac{1}{2}} + 4 \cdot 11^{\frac{1}{2}}
|
1,448 |
\frac32x=n\implies x=\frac23n
|
31,354 |
|x| = \|\frac12 \cdot (x + y) + (x - y)/2\| \leq (|x + y| + |x - y|)/2
|
19,388 |
(g^2 + x^2)\cdot (h^2 + f \cdot f) = (x\cdot f + h\cdot g)^2 + (h\cdot x - f\cdot g)^2
|
-5,689 |
\frac{2}{(y + 1)\cdot (6\cdot (-1) + y)}\cdot y = \dfrac{y\cdot 2}{y \cdot y - y\cdot 5 + 6\cdot (-1)}
|
21,831 |
0 = d + 0 + 0 \implies d = 0
|
-25,790 |
\dfrac{1}{7}\cdot 10/4 = 10/28
|
13,895 |
x_2^2 + x_1 \cdot x_1 + 2 \cdot x_1 \cdot x_2 = \left(x_2 + x_1\right)^2
|
46,371 |
\cos^4\left(x\right) = \cos^2(x) \cdot (1 - \sin^2(x)) = \cos^2\left(x\right) - \cos^2(x) \cdot \sin^2(x)
|
-10,703 |
\tfrac{4}{4}*\dfrac{3}{x} = \frac{12}{x*4}
|
19,490 |
\left(800^2 + 800^2\right)^{1 / 2} = 2^{\frac{1}{2}}*800 \approx 1131
|
-23,477 |
\dfrac{5}{16} = \frac{5}{2} \cdot 1/8
|
19,376 |
\frac{1}{m\cdot (m + (-1)) ((-1) + m)!} = \frac{1}{m! \left(m + (-1)\right)}
|
4,588 |
z^5 + (-1) = \left(z + (-1)\right) (1 + z^4 + z^3 + z^2 + z)
|
-12,039 |
14/15 = s/\left(4*\pi\right)*4*\pi = s
|
16,543 |
3^x + 3^z = 3^x*(1 + 3^{z - x})
|
2,982 |
(-w + v)\cdot \left(v - w\right)^x = (-w + v)\cdot (v - w)^x
|
6,615 |
\sin{y} = \cos{y} rightarrow (-e^{-yi} + e^{iy})/(2i) = (e^{-yi} + e^{yi})/2
|
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