id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
11,153 |
2 \cdot 2^2 + 4 \cdot (-1) = 8 + 4 \cdot (-1) = 4
|
4,250 |
4^1 + x^4 = (1 + (1 + x)^2) \cdot ((x + (-1))^2 + 1)
|
11,321 |
\frac{\dfrac{1}{\sqrt{5} + 2}\cdot (\sqrt{5} + 2)}{\sqrt{5} + 2\cdot (-1)} = \dfrac{1}{\sqrt{5} + 2\cdot (-1)}
|
18,980 |
1 + \sqrt{5} \cdot i = 1 + \sqrt{-5}
|
27,503 |
0\le-x<1\implies \tan(\arcsin(x))=-\tan(-\arcsin(x))=-\tan(\arcsin(-x))=-\frac{-x}{\sqrt{1-x^2}}
|
43,839 |
x^2 = x x
|
-7,392 |
1/4\cdot 3/2 = \frac38
|
1,779 |
f^{\frac{3}{2}} = (f^{1/2})^3
|
35,959 |
240 = 3 \cdot (-1) + 3^5
|
44,652 |
\left(-5\right) * \left(-5\right) = 25 \geq 0
|
18,432 |
\frac{1}{gx} = 1/(gx)
|
-6,466 |
\tfrac{1}{\left(x + 7(-1)\right)*2}4 = \frac{1}{14 (-1) + 2x}4
|
-18,318 |
\frac{56\cdot (-1) + s^2 - s}{s \cdot s - s\cdot 9 + 8} = \frac{(8\cdot (-1) + s)\cdot (s + 7)}{(s + (-1))\cdot \left(8\cdot \left(-1\right) + s\right)}
|
15,879 |
\frac{\mathrm{d}}{\mathrm{d}x} (\cos(x) + \sin(x)) = -\sin\left(x\right) + \cos(x) = u \Rightarrow u^2 = -\sin\left(2x\right) + 1
|
34,134 |
\sin(90) = 1 = 2\cdot \sin(30) = 2\cdot 0.5 = 1
|
14,692 |
\|v\|^2 = \sqrt{v_1^2 + v_2 \cdot v_2 + v_3^2} \cdot \sqrt{v_1^2 + v_2 \cdot v_2 + v_3^2} = v_1^2 + v_2^2 + v_3^2
|
44,752 |
\left(\frac{1}{27}\cdot (c_1^3 + c_2 \cdot c_2 \cdot c_2 + g^3 + 24)\right)^{1/3} = \frac13\cdot (c_1 + c_2 + g) \leq (\frac{1}{27}\cdot (c_1^3 + c_2^3 + g \cdot g \cdot g))^{1/27}
|
4,171 |
\frac{1}{n + 1} = \frac{1}{(1 + n)!}*n!
|
-3,354 |
13^{1/2}\cdot 9 = 13^{1/2}\cdot (4 + 3 + 2)
|
13,819 |
2^{1 / 2} = \frac{1}{2^{\dfrac{1}{2}}}\cdot 2
|
218 |
1/x - 1/b = \dfrac{b}{x b} - x/(x b) = (x - b)/\left(x b\right)
|
-8,922 |
-1^5 = (-1) \cdot (-1) \cdot \left(-1\right) \cdot (-1) \cdot \left(-1\right)
|
11,209 |
\left(b + 1\right)\cdot (b^{\left(-1\right) + x} - b^{2\cdot \left(-1\right) + x}\cdot ...\cdot ... + 1) = b^x + 1
|
35,329 |
10/8991 + \frac{1}{333} = 1/243
|
15,226 |
2\times \frac{100}{2}\times (100 + 1) + 100 = 100 + 10100
|
89 |
{8 \choose 3}\cdot (5/3 + \frac14\cdot 5)\cdot {7 \choose 2} = 3430
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-19,213 |
\tfrac{4}{15} = \tfrac{Y_q}{100 \cdot \pi} \cdot 100 \cdot \pi = Y_q
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8,928 |
\frac{1}{1 + 7 + 6} \cdot 6 \cdot \frac{5}{5 + 4} = \frac{1}{126} \cdot 30
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7,035 |
y x = 1 \implies \frac{1}{x} = y
|
39,032 |
q*(-q + 1) = q - q^2
|
-3,243 |
\sqrt{10} = \sqrt{10}\cdot \left(3 + 2\cdot (-1)\right)
|
-26,356 |
-1/4 \left(-1/4\right) = 1/16
|
25,371 |
\pi*20 = 8*\pi + 8*\pi + 4*\pi
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36,502 |
\frac{1}{2} + 1/3 + 1/9 + 1/18 = 1
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-22,192 |
54*(-1) + p^2 - p*3 = (p + 6)*(p + 9*(-1))
|
21,360 |
(z^2 + y * y) * (z^2 + y * y) = (z * z - y^2)^2 + (2zy) * (2zy) = 5^2 + 12^2 = 13 * 13 \Rightarrow z^2 + y^2 = 13
|
-19,420 |
1/2 \cdot 3/(1/6) = 3/2 \cdot 6/1
|
-4,115 |
\frac{y \cdot y\cdot 18}{90\cdot y \cdot y}\cdot 1 = \frac{1}{y \cdot y}\cdot y^2\cdot 18/90
|
11,111 |
15 = (1^2 + 1^2 + 1^2)\cdot (2^2 + 1^2 + 0^2)
|
24,261 |
g + f := f + g
|
18,821 |
\int (p^2 + \frac{2}{p^2})\,\mathrm{d}p = \int \frac{1}{p^2}\cdot \left(p^4 + 2\right)\,\mathrm{d}p
|
40,816 |
2^2\cdot 239 = 956
|
-2,688 |
4 \cdot \sqrt{3} = \sqrt{3} \cdot (3 + (-1) + 2)
|
19,311 |
\arctan{y} = c + x \Rightarrow \tan(x + c) = y
|
40,725 |
n^2=\frac{\frac{(2n)(2n)}{2}}{2}=\frac{\frac{(2n+1)(2n)}{2}-n}{2}=\frac{\binom{2n+1}{2}-n}{2}
|
16,332 |
-2^3 + x^3 = (2\left(-1\right) + x) \left(x^2 + x\cdot 2 + 2^2\right)
|
831 |
\tan{C\cdot E\cdot M} = M\cdot E/(E\cdot C) \implies M\cdot E\cdot C = \operatorname{atan}\left(M\cdot E/(C\cdot E)\right)
|
33,045 |
|(f,g)|=|(g,f)|\le \|f\|_2\|g\|_2
|
723 |
x^3 - b^2 \cdot b = (-b + x) \cdot \left(b^2 + x^2 + x \cdot b\right)
|
28,589 |
112 = 4\cdot \binom{8}{2}
|
-23,580 |
1/7 = \frac{5}{5} \cdot \frac{1}{7}
|
2,091 |
z + \alpha/2 + \frac{\alpha}{2} = z + \alpha
|
9,106 |
3/8 \cdot \frac12 + \dfrac12 \cdot \tfrac26 = \dfrac{1}{48} \cdot 17
|
21,919 |
2 + 3*(1 + x) = 5 + x*3
|
-30,245 |
z^2 - z\cdot 2 + 1 = (z + (-1))\cdot (z + (-1))
|
-10,441 |
-\frac{1}{6*x + 18*(-1)}*20 = -\tfrac{10}{3*x + 9*(-1)}*\frac22
|
9,062 |
13 = 2 + 3 + c_3 \Rightarrow c_3 = 8
|
19,731 |
\sum_{i=1}^a x = \sum_{i=1}^x a
|
21,703 |
3 + 3\cdot ((-1) + y) + 3\cdot (\left(-1\right) + y)^2 + (y + (-1))^3 = y \cdot y \cdot y + 2
|
12,716 |
x * x^2 - x*2 + 2*(-1) = -x*2 + \left(-1\right) + \left(1 + x^2 + x\right)*\left((-1) + x\right)
|
18,362 |
c + 3*\left(-1\right) = -(3 - c)
|
26,570 |
-(17 - 3 \cdot 34^{1 / 2}) \cdot (17 + 34^{\frac{1}{2}} \cdot 3) = 17
|
10,212 |
(a + c)^2 = a^2 + 2*a*c + c^2
|
-5,253 |
0.61*10^{0 - -3} = 0.61*10 10 10
|
11,280 |
\frac{1}{\frac{1}{b\cdot \frac{1}{\frac{1}{h}}}}\cdot a = \frac{a}{1/h}\cdot \frac{1}{\dfrac1b}
|
-7,778 |
\left(a - b\right) \cdot (a + b) = -b^2 + a^2
|
23,795 |
n^6 - n^4\cdot 3 + n n\cdot 3 + (-1) = (n n + (-1))^3
|
28,757 |
3\cdot 12\cdot 11\cdot 4\cdot (10 + 9 + 3) = 34848
|
2,373 |
459/400 = -\dfrac{1}{5^2} + 1 + \frac{1}{2 \cdot 2} - \frac{1}{4 \cdot 4}
|
17,756 |
1.414213562373 \cdot \dotsm = 2^{1/2}
|
-9,750 |
0.01 \cdot \left(-15\right) = -\frac{1}{100} \cdot 15 = -0.15
|
14,433 |
\tan{j} = \sin{j}/\cos{j}
|
28,122 |
A_i \cdot A_{1 + i} = A_{i + 1} \cdot A_i
|
-7,788 |
4\cdot i/2 + 8/2 = \frac{1}{2}\cdot (8 + 4\cdot i)
|
13,309 |
a^2 - x^2 = \left(a + x\right) \cdot (-x + a)
|
-6,750 |
\frac{1}{100}6 + \frac{1}{10}8 = 6/100 + \frac{80}{100}
|
22,335 |
1 + \frac{z}{-z + 1} = \frac{1}{-z + 1}
|
-20,559 |
\frac{x\cdot 45}{(-10)\cdot x} = -9/2\cdot ((-5)\cdot x)/\left(x\cdot (-5)\right)
|
-24,852 |
\frac{u}{3} - \frac{w}{2} = -1/2 \cdot \left(u/3 + w/2\right) + 1 = ((-1) \cdot u)/6 - \frac14 \cdot w + 1
|
1,730 |
f_{i_l}\cdot f_{i_k} = f_{i_l}\cdot f_{i_k}
|
4,659 |
\dfrac{E}{x} = \frac{E}{x}
|
19,441 |
x\cdot v_2/(v_4) = x\cdot v_2/(v_4)
|
13,834 |
xx^{n + (-1)} = x^n
|
1,961 |
\frac{1}{1 - x} = \dfrac{1 + 0 \cdot \left(-1\right)}{1 - x}
|
25,405 |
1 + 2^{30} = 5*5*13*41*61*1321
|
49,431 |
f = 0 + f
|
-3,065 |
7^{\frac{1}{2}} \cdot 4 + 7^{1 / 2} \cdot 5 = 25^{\frac{1}{2}} \cdot 7^{\frac{1}{2}} + 7^{1 / 2} \cdot 16^{1 / 2}
|
27,236 |
-\frac{\pi}{4} + \frac34*\pi = \frac{\pi}{4}*2
|
-7,117 |
\frac{3}{10}*\frac{2}{9} = 1/15
|
14,368 |
2 = \left\{\left( 2, 0\right), \dots, ( 3, 1), ( 4, 2)\right\}
|
6,059 |
\frac{\left(-1\right) + m \cdot 2}{m \cdot 2 + 3} = 1 - \frac{4}{3 + 2 \cdot m}
|
33,048 |
298\cdot (-1) + 1000 + (-1) + 193\cdot (-1) = 508
|
-21,839 |
8/3 + \frac{9}{5} = \frac{8*5}{3*5} + \frac{9*3}{5*3} = 40/15 + \frac{1}{15} 27 = \dfrac{1}{15} (40 + 27) = 67/15
|
37,987 |
Z^U\cdot x\cdot Z = Z^U\cdot z \implies \dfrac{Z^U\cdot z}{Z\cdot Z^U}\cdot 1 = x
|
27,684 |
9\cdot \left(-1\right) + 10 = \dfrac13\cdot (2 + 1)
|
-4,201 |
\tfrac{88}{11}\cdot t/t = t\cdot 88/(11\cdot t)
|
26,173 |
\sum_{i=1}^\infty |-b_i| = \sum_{i=1}^\infty |b_i|
|
8,578 |
\sin(3\cdot y) = \sin(2\cdot y + y) = \sin(2\cdot y)\cdot \cos(y) + \cos(2\cdot y)\cdot \sin\left(y\right)
|
-573 |
-4 \cdot \pi + \pi \cdot 14/3 = \pi \cdot \frac23
|
-4,261 |
\frac{1}{a^5} \times a^2 \times a \times 132/144 = \frac{132 \times a^3}{a^5 \times 144}
|
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