id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
37,074 |
r_1 \cdot r_2 = r_2 \cdot r_1
|
6,676 |
2 \times \cos(s) \times \sin(s) = \sin(2 \times s)
|
23,145 |
1! + 2! + ... + l! + (l + 1)! \leq 2*l! + (l + 1)! = \left(l + 3\right)*l! \leq 2*(l + 1)*l!
|
3,595 |
b + (-1) = a + (-1)\Longrightarrow b = a
|
-16,352 |
80^{1 / 2}\cdot 8 = 8(16\cdot 5)^{1 / 2}
|
37,055 |
22\cdot 4 + 2\cdot 6 = 100
|
150 |
\left(y, z \geq 0 \Rightarrow y \times 2 = z \times 2\right) \Rightarrow z = y
|
8,340 |
\left(-x - 1\right)\cdot (-1 - x) = x^2 + 1 + x\cdot 2
|
-18,854 |
\frac{1}{2}18 = 9
|
17,181 |
3\cdot 2\cdot t + 1 = 1 + 6\cdot t
|
23,765 |
\sec{x} \tan{x} = \frac{d}{dx} \sec{x}
|
47,726 |
687 = 3\times 229
|
25,989 |
-\pi/3 + 2\pi = -\tan^{-1}(\sqrt{3}) + \pi*2
|
1,789 |
32 + 7 \left(-1\right) = 25
|
10,470 |
25\cdot \sqrt{2} = \sqrt{1250}
|
-20,875 |
7/7 ((-1) + k)/(k*(-4)) = \frac{7\left(-1\right) + 7k}{\left(-1\right)*28 k}
|
-22,221 |
(x + 6)\cdot (x + \left(-1\right)) = 6\cdot (-1) + x^2 + 5\cdot x
|
6,743 |
\frac{1}{2\cdot \tfrac{1}{1 - y^2}\cdot (1 + y + 1 - y)} = \frac{2}{2\cdot (1 - y^2)} = \dfrac{1}{1 - y^2}
|
23,770 |
3^{n + 2\cdot (-1)} = 3^{n + (-1)}/3 = 3^{n + (-1)}/3
|
13,790 |
3!\cdot 2!\cdot {5 \choose 3} = 120
|
46,326 |
10 + 10 (-1) = 0 \neq 10
|
11,413 |
\sqrt{2}\cdot 11 + \sqrt{3}\cdot 9 = (\sqrt{3} + \sqrt{2})^3
|
1,328 |
x \cdot x^2 \cdot 2 \cdot 2 \cdot x^2 = x^{2 + 2 + 1} \cdot 2 \cdot 2
|
-13,090 |
-0.486 = -\dfrac{1}{0.07} \cdot 0.03402
|
-3,129 |
9*3^{1 / 2} = 3^{\frac{1}{2}}*(5 + 4)
|
-4,440 |
\frac{9*x + 6*(-1)}{8*(-1) + x^2 - 2*x} = \frac{1}{x + 4*(-1)}*5 + \frac{1}{x + 2}*4
|
26,497 |
2 = (\sqrt{2})^2 = \left(2^{1/4}\right)^4 = ...
|
9,799 |
(\sqrt{4 x^2 - 5 x})^2 - (2 x) (2 x) = 4 x^2 - 5 x - 4 x^2 = -5 x
|
31,161 |
z = -i \pm \sqrt{2} i \Rightarrow |z| = -1 + \sqrt{2}
|
20,786 |
\dfrac{0}{0!} = \tfrac{0}{1} = 0
|
3,138 |
f \geq 2*(2 - m + f) \implies 4*\left(-1\right) + m*2 \geq f
|
9,289 |
\left(-1\right)^{\frac{2}{4}} = \left(-1\right)^{1/2} = i
|
27,670 |
\cot(X) - \tan(X) = (\cos^2(X) - \sin^2(X))/\left(\sin(X)*\cos(X)\right) = 2*\cot(2*X)
|
8,861 |
h^3 + g^3 = (g + h)\cdot (h^2 - g\cdot h + g^2)
|
8,224 |
\frac{1}{81} = \frac{1}{6^3} \cdot (1 + 5/6 + \dfrac56)
|
-2,104 |
\frac{1}{12} \cdot 17 \cdot \pi + 0 = 17/12 \cdot \pi
|
-19,425 |
\frac{\frac{1}{6}}{9\cdot \frac{1}{4}}\cdot 5 = \frac49\cdot 5/6
|
37,132 |
9660 = 5^2\cdot 3\cdot 2^7 + 60
|
-20,939 |
1/(k*7)*k*7/2 = 7*k/(14*k)
|
953 |
\left(-i \cdot d = (d^2 + (-1))^{1 / 2} rightarrow d^2 + (-1) = -d^2\right) rightarrow d = -\frac{1}{2^{\frac{1}{2}}}
|
11,556 |
\frac154 = 0.8
|
-16,591 |
2\cdot 112^{1/2} = 2\cdot (16\cdot 7)^{1/2}
|
6,412 |
(-1) + X^2 = \left((-1) + X\right) (1 + X)
|
8,078 |
(-2)^2 - 4 \cdot 2 = 4 + 8\left(-1\right) = -4 \lt 0
|
-21,043 |
6/12 = 3/3\cdot \frac24
|
3,150 |
\dfrac{1}{x + 11}\cdot \left(x \cdot x + x\cdot 9 + c\right) = \frac{22 + c}{x + 11} + x + 2\cdot (-1)
|
19,452 |
6 + x * x - x*5 = \left(3(-1) + x\right) (2(-1) + x)
|
21,768 |
5^{2 + 2k} = 5 * 5*5^{k*2}
|
40,630 |
8 = 20 + 12\times (-1)
|
-13,329 |
\dfrac{1}{8 + 3\cdot (-1)}\cdot 35 = 35/5 = 35/5 = 7
|
16,765 |
(1 + d) \cdot (b + (-1)) + 1 = d \cdot b - d + b
|
-9,123 |
36 \cdot q + 12 \cdot (-1) = -3 \cdot 2 \cdot 2 + 2 \cdot 2 \cdot 3 \cdot 3 \cdot q
|
-9,406 |
2 \times 2 \times 2 \times 2 \times 3 + 2 \times 2 \times 3 \times 3 \times x = 48 + 36 \times x
|
16,125 |
(x - y + 1) (y + x) = x^2 - y^2 + x + y
|
-6,058 |
\frac{1}{4\cdot a + 40\cdot (-1)}\cdot 2 = \frac{2}{\left(a + 10\cdot (-1)\right)\cdot 4}
|
-3,819 |
a^5/a = a*a*a*a*a/a = a^4
|
-6,423 |
\tfrac{2}{r \cdot 2 + 2} = \tfrac{2}{2(1 + r)}
|
3,861 |
2^3 - 2*3 + 2(-1) = 0
|
-19,581 |
\frac{1/8 \cdot 3}{5 \cdot 1/9} = \frac15 \cdot 9 \cdot 3/8
|
36,574 |
\binom{p + 3}{p} = \binom{p + 3}{3} = (p + 1) \cdot (p + 2) \cdot \left(p + 3\right)/3!
|
5,693 |
x^{x^{x^{\ldots}}} = n rightarrow x = n^{\frac{1}{n}}
|
13,274 |
\tfrac{1}{2^2} = \frac{2^0}{2^2} = \dfrac14
|
12,394 |
\frac{\partial}{\partial x} (g*d) = g*\frac{\mathrm{d}d}{\mathrm{d}x} + d*\frac{\mathrm{d}g}{\mathrm{d}x}
|
-9,354 |
66 + 11\cdot x = x\cdot 11 + 2\cdot 3\cdot 11
|
9,536 |
0 = 1 + y + y^2 + ... + y^{t + (-1)} = \frac{y^t + (-1)}{y + (-1)}\Longrightarrow y^t = 1
|
28,783 |
f = z\Longrightarrow |f| = |z|
|
38,594 |
3796 = \binom{52}{3} + 18304*\left(-1\right)
|
19,459 |
(2^{(-1) + x})^2 = 2^{2\cdot (-1) + x\cdot 2}
|
19,007 |
1/4 + \dfrac14 = \dfrac12
|
40,737 |
2 - 4^{1/2} = 0
|
2,675 |
\tan(y) = \sin(y)/\cos\left(y\right) = 1/\cot(y)
|
29,667 |
\binom{G + x}{x} = \binom{x + G}{G}
|
25,353 |
-7/24 = \cot(D)\Longrightarrow -24/7 = \tan(D)
|
31,344 |
\sum_{m=0}^N ar^m = a + \sum_{m=1}^N ar^m = a + r\sum_{m=0}^{N + (-1)} ar^{m + 1}
|
36,619 |
(((-1) + z)^2 + 1) (\left(1 + z\right)^2 + 1) = 4 + z^4
|
6,190 |
\frac{1}{6}(2(n + 1) + 1) (n + 1 + 1) (n + 1) = 1^2 + 2^2 + 3^2 + \dotsm + n^2 + (n + 1)^2
|
22,440 |
\frac{1}{(-j + x)!\cdot j!}\cdot x! = {x \choose j}
|
-5,408 |
\frac{6.6}{10} = \tfrac{6.6}{10}*10^6 = 6.6*10^5
|
-9,669 |
13/100*\frac{21}{50} (-17/25) = 13*21 \left(-17\right)/(100*50*25) = -4641/125000
|
24,702 |
2*\left(g_k + 2*(-1)\right) = 2*g_k + 4*(-1) \gt g_k
|
-19,213 |
\frac{1}{15}*4 = \dfrac{1}{100*\pi}*A_s*100*\pi = A_s
|
3,050 |
\sqrt{-1} = \tfrac{1}{2^{1/4}}\cdot i\cdot 2^{1/4}
|
2,437 |
|Fy - g|^2 = (Fy - g)^p*(Fy - g) = y^p F^p Fy - 2y^p F^p g + g^2
|
38,312 |
|-c + x| = |-x + c|
|
15,894 |
h' k' kc = ck h' k'
|
-4,851 |
2.35*10 = 2.35*10*10^2 = 2.35*10 * 10 * 10
|
13,520 |
(\frac{1}{x^4} \cdot y^3)^{\frac14} = \frac{y^{3 \cdot 1/4}}{x^{4 \cdot 1/4}} = \frac{y^{3/4}}{x}
|
10,885 |
1/2 + \frac12 + \frac12 = \frac32 = 1.5
|
-1,855 |
9/4*\pi = \tfrac{\pi}{2} + \pi*\frac{7}{4}
|
-13,240 |
1 - 9*3 + 56/8 = 1 - 9*3 + 7 = 1 + 27*(-1) + 7 = -26 + 7 = -19
|
10,196 |
2*(-1) + 2^G = 2^G + (-1) + (-1)
|
-22,081 |
\tfrac35 = 6/10
|
39,620 |
\frac13288 = 96
|
5,983 |
0 = 1 + x_1 \times 2 + \cos(1)\Longrightarrow -\dfrac{1}{2} \times \left(1 + \cos(1)\right) = x_1
|
26,072 |
n \cdot n! = (n + 1 + \left(-1\right)) \cdot n! = (n + 1)! - n!
|
25,958 |
e \times \frac{1}{e} \times H = e \times H \times e = H
|
13,327 |
r + (-1) + j + 2\left(-1\right) = r + j + 3(-1)
|
10,282 |
[a] \cdot [b] := [a \cdot b]
|
8,182 |
1/(d*x) = \frac{1}{d*x}
|
-20,106 |
3/5 \cdot \frac{t \cdot 3}{t \cdot 3} = \frac{9 \cdot t}{15 \cdot t}
|
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