id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
36,032 |
\cos{3x} = \cos^3{x} \cdot 4 - 3\cos{x}
|
455 |
205 + 195 (-1) = \frac{1}{\sqrt{20}}24 = 1.862
|
-4,720 |
\frac{24 - 8y}{y^2 - y*6 + 8} = -\frac{1}{2\left(-1\right) + y}4 - \frac{4}{y + 4(-1)}
|
1,844 |
6 = (1 + \sqrt{7})\cdot (\sqrt{7} + \left(-1\right))
|
12,903 |
a^y\times a^z = a^{y + z}
|
-2,130 |
\pi/3 - \pi \frac{3}{4} = -\pi \frac{5}{12}
|
-29,368 |
(s + 2) \times (s + 3) = s \times s + 3 \times s + 2 \times s + 6 = s \times s + 5 \times s + 6
|
1,423 |
6!*{5 \choose 1}*5!*2 = 864000
|
27,126 |
10^{1 + m} = 10^m\cdot 10
|
-28,780 |
\tan^2(x) = (-1) + \sec^2\left(x\right)
|
7,188 |
-\frac{1}{49}*24 = -24/49
|
1,070 |
z^2 - (f_1 + f_2)\cdot z + f_1\cdot f_2 = (z - f_1)\cdot (-f_2 + z)
|
-17,428 |
72 - 58 = 14
|
4,618 |
S_{m, k} + S_{k,x} = S_{m,x} \Rightarrow |S_{m, k}| - |S_{k, x}| \leq |S_{m, x}|
|
24,033 |
1/2 + 2/7 + \frac{2}{5} = 83/70
|
15,060 |
\sqrt{3}\times 0 + 11 = 11
|
207 |
AA^Q = A^Q A
|
36,240 |
\dfrac{28!}{22! \cdot 6!} = \binom{28}{6}
|
24,836 |
g \cdot g - A \cdot A = (A + g)\cdot (g - A)
|
28,097 |
-b + a = (\sqrt{a} + \sqrt{b}) \cdot (\sqrt{a} - \sqrt{b})
|
13,233 |
\int (1+\cos(x))^3 = \frac{\frac{\sin(3x)}{3}+6\frac{\sin(2x)}{2}+15 \sin(x) + 10x}{4} + c = \frac{\sin(3x)}{12} + \frac{3\sin(2x)}{4} + \frac{15 \sin(x)}{4} + \frac{5x}{2} + c
|
55,227 |
{13 \choose 1} = 13
|
36,358 |
99 = 81 \cdot (-1) + 180
|
26,127 |
(X + E) Y = YE + YX
|
16,625 |
x^{l_2} \cdot x^{l_1} = x^{l_1 + l_2}
|
13,737 |
9 \cdot x^2 + 36 \cdot (-1) = 3 \cdot x^2 - 6 \cdot 6 = (3 \cdot x + 6) \cdot \left(3 \cdot x + 6 \cdot (-1)\right) = 3 \cdot (x + 2) \cdot (3 \cdot x + 6 \cdot (-1)) = 9 \cdot (x + 2) \cdot (x + 2 \cdot (-1))
|
17,069 |
2 \cdot s^2 + s^2 = s^2 \cdot 3
|
-22,235 |
(k + 9) \cdot (k + 6) = 54 + k \cdot k + 15 \cdot k
|
29,374 |
\left(1 + k\right)^2 = k^2 + 2 \cdot k + 1
|
14,171 |
n + n + 1 + \ldots + n + 10 = 11 \cdot n + 55 = 11 \cdot (n + 5)
|
10,983 |
\dfrac{(\dfrac{k}{2})^2}{\frac{k}{2} + k} = \frac{1}{6}\cdot k
|
11,432 |
3(m + m^2) = m^2 \cdot 3 + 3m
|
-24,456 |
(3*2)^2 = 6 * 6 = 6^2 = 36
|
21,264 |
|\frac{1}{z^2 + 1} - \frac{1}{1 + u^2}| = |\frac{-z \cdot z + u^2}{(z^2 + 1) \cdot (u^2 + 1)}|
|
2,290 |
x + (2 - x)/2 = \frac{2}{2} \cdot x + (2 - x)/2 = \frac{1}{2} \cdot (x + 2)
|
-20,967 |
\dfrac{1}{6}6 \dfrac{1}{(-2) q}\left(-q\cdot 7 + 4\right) = \frac{1}{(-1)\cdot 12 q}(24 - 42 q)
|
31,685 |
3^{119}/4 = \dfrac{1}{4}\cdot 599003433304810403471059943169868346577158542512617035467
|
14,257 |
\cot(3\cdot \pi/2 - x) = \cot(\pi - x - \pi/2) = -\cot(x - \pi/2) = \cot(\pi/2 - x) = \tan{x}
|
8,830 |
\cos(\beta) \sin(\alpha) + \sin(\beta) \cos(\alpha) = \sin(\alpha + \beta)
|
5,757 |
\sin^4\left(x\right) + \cos^4\left(x\right) = (\sin^2(x) + \cos^2(x))^2 - 2\cdot \sin^2(x)\cdot \cos^2(x) = 1 - 2\cdot \sin^2(x)\cdot \cos^2(x)
|
13,021 |
\frac{42}{q \cdot q + q\cdot 7} = -\dfrac{6}{q + 7} + 6/q
|
-30,259 |
(z + 3)*(4*(-1) + z) = z^2 - z + 12*(-1)
|
30,403 |
\dfrac{1}{x + 3} (x^2 + 5 x + 7) = x + \frac{2 x + 7}{x + 3} = x + 2 + \frac{1}{x + 3}
|
6,473 |
\dfrac{2 \times x + 1}{2 \times n + 2} = (\tfrac{x}{n + 1} + \frac{x + 1}{n + 1})/2
|
5,709 |
1 - \frac{95}{100} = \dfrac{5}{100}
|
12,859 |
a^{z + x} = a^z \times a^x
|
8,194 |
\left(0 = (-1) + q^2 - q\cdot 2 \Rightarrow -2\cdot q = -q^2 + 1\right) \Rightarrow -1 = \frac{2\cdot q}{1 - q^2}
|
32,114 |
(\left(-1\right) + f) \cdot a - f = -f + a \cdot f - a
|
12,444 |
\dfrac{52!}{25! (25 (-1) + 52)!} = 477551179875952
|
12,242 |
\cot{C} = \tan(\tfrac{1}{2}\pi - C)
|
18,902 |
9 \cdot 9 + 65 \cdot \left(-1\right) = 16
|
-6,394 |
\frac{3}{18 \cdot (-1) + r \cdot 3} = \frac{3}{3 \cdot (r + 6 \cdot (-1))}
|
-7,541 |
\frac{-37 - 5i}{i*5 + 3} = \frac{-37 - 5i}{3 + i*5} \dfrac{3 - 5i}{3 - i*5}
|
10,492 |
\omega = \frac{5^{1/3}*\omega}{5^{\frac{1}{3}}}
|
29,331 |
\frac13\cdot \left(6 + 1 + 2\right) = 3
|
24,577 |
3 \cdot y^2 + 3 \cdot y + 6 \cdot (-1) = 3 \cdot (y^2 + y + 2 \cdot \left(-1\right)) = 3 \cdot \left(y + (-1)\right) \cdot (y + 2)
|
-4,683 |
-\frac{4}{z + 2\cdot (-1)} + \dfrac{1}{3 + z}\cdot 3 = \frac{-z + 18\cdot (-1)}{z \cdot z + z + 6\cdot (-1)}
|
9,792 |
x*m = 1 + \frac{7}{10}*(x*m - x) + 3/10*(x*m + x) = x*m + 1 - 2/5*x
|
-5,462 |
\tfrac{1}{3\cdot \left(p + 10\right)}\cdot 2 = \frac{2}{p\cdot 3 + 30}
|
34,947 |
z \approx y \Rightarrow z \approx y
|
29,890 |
\dfrac{\left(-1\right) + z}{(\left(-1\right) + z)^2} = \frac{1}{(-1) + z}
|
15,878 |
(n^2 + n/2)^2 = n^4 + n^2 \cdot n + \frac{n^2}{4} < n^4 + n^3 + n^2 + n + 1
|
9,588 |
F = F \cap x \Rightarrow \{F, x\}
|
6,842 |
{j + 2*x \choose j} = {j + x*2 \choose x*2}
|
-29,716 |
\frac{\mathrm{d}}{\mathrm{d}x} x^k = k*x^{k + \left(-1\right)}
|
-20,868 |
\frac{14}{7 - 56\cdot b} = 7/7\cdot \tfrac{1}{1 - 8\cdot b}\cdot 2
|
34,302 |
17^{\frac{1}{2}} = \dfrac{1}{17^{1 / 2}} \cdot 17
|
38,014 |
7 = 10 - 3
|
4,552 |
-\dfrac{1}{x \cdot x} \cdot 7 + 1 = \frac{1}{x^3} \cdot (-7 \cdot x + x^2 \cdot x)
|
21,063 |
16/3 = 1/6\cdot 4 + \frac12\cdot 6 + \frac{1}{3}\cdot 5
|
7,336 |
30/81 = \dfrac{6}{9}*5/9
|
-7,223 |
10^{-1} = \frac{4}{16} \times 6/15
|
-20,677 |
-8/3 \cdot \frac{2 \cdot (-1) - 8 \cdot m}{2 \cdot (-1) - m \cdot 8} = \frac{16 + m \cdot 64}{6 \cdot (-1) - 24 \cdot m}
|
9,647 |
\cos(\frac{105}{3}) = \cos\left(35\right)
|
15,720 |
\max{e,x,m} = \max{e,\max{x, m}} = \max{\max{e,x},m}
|
-3,218 |
112^{\frac{1}{2}} + 175^{1 / 2} - 7^{\frac{1}{2}} = (16\cdot 7)^{1 / 2} + (25\cdot 7)^{\frac{1}{2}} - 7^{\frac{1}{2}}
|
-458 |
e^{17\cdot π\cdot i/3} = \left(e^{\frac{i}{3}\cdot π}\right)^{17}
|
16,656 |
\frac{\frac{3}{4}*\frac{1}{4} 3}{2} = 9/32
|
10,059 |
32\cdot 2/(2\cdot 72) = \tfrac{1}{72}\cdot 32
|
-4,761 |
\frac{17 \cdot (-1) - x}{3 \cdot (-1) + x \cdot x - x \cdot 2} = -\frac{5}{x + 3 \cdot \left(-1\right)} + \frac{1}{1 + x} \cdot 4
|
-3,415 |
4\sqrt{6} = (5 + 3 + 4(-1)) \sqrt{6}
|
14,556 |
\int a \cdot (f_1 T + \alpha T f_2)\,dy = \int a T \cdot \left(f_1 + \alpha f_2\right)\,dy
|
-19,738 |
\dfrac{1}{8} \cdot 35 = \frac{35}{8}
|
17,752 |
(p + 2\cdot \left(-1\right))! = \frac{(p + (-1))!}{\left(-1\right) + p}
|
20,409 |
(-1) + t^3 = (t + (-1)) \cdot \left(t^2 + t + 1\right)
|
30,830 |
2^b \cdot 2^d = 2^{d + b}
|
-4,157 |
63/35*\frac{1}{y^5}*y^3 = \frac{63*y^3}{y^5*35}
|
21,632 |
x = 2\dfrac12x
|
-22,941 |
\frac{63}{54} = \frac{9 \cdot 7}{9 \cdot 6}
|
5,220 |
( (a + 5) \times 2, 3 \times (a + 5), 17) = ( a \times 2 + 10, 15 + 3 \times a, 17)
|
6,133 |
m\cdot 3 - x\cdot 3 = \left(m - x\right)\cdot 3
|
-24,888 |
\frac{1}{18} = \dfrac{1}{6\pi}s \cdot 6\pi = s
|
-6,746 |
\frac{7}{100} + \frac{1}{100} \cdot 80 = 8/10 + \frac{1}{100} \cdot 7
|
26,531 |
\frac{1}{h^{-c}} = h^c
|
-3,819 |
a^5/a = \frac{a*a*a*a*a}{a} = a^4
|
9,417 |
\frac12 \cdot (1 + 3) = 4/2 = 2
|
-18,391 |
\frac{1}{x \cdot 7 + x^2} \cdot (42 + x^2 + x \cdot 13) = \frac{1}{(x + 7) \cdot x} \cdot (x + 6) \cdot \left(7 + x\right)
|
-22,248 |
20 + x \cdot x - x\cdot 12 = (2(-1) + x) (x + 10 \left(-1\right))
|
8,074 |
\frac{1}{2 \cdot u^3} = \dfrac{1}{2 \cdot u^3}
|
17,384 |
1 + y^2 - y = (-1/2 + y)^2 + 3/4
|
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