id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
3,828 |
b*a = c \Rightarrow b*a = c,b = a*c
|
-1,655 |
-3/2\cdot \pi + 2\cdot \pi = \pi/2
|
13,941 |
f = 2 \cdot s\Longrightarrow f/2 = s
|
-10,303 |
-\frac{24}{p\cdot 8 + 20} = -\frac{6}{2\cdot p + 5}\cdot \frac44
|
1,411 |
\left(\operatorname{asin}(1) = y \Rightarrow 1 = \sin(y)\right) \Rightarrow y = \pi/2
|
11,376 |
\dfrac{1}{\vartheta} \cdot (e^\vartheta + (-1)) = z \implies \vartheta \cdot z + 1 = e^\vartheta
|
-11,536 |
10\cdot i + 40 = 25 + 15 + i\cdot 10
|
-10,683 |
\frac{1}{5\omega}\left(2\omega + 8\right) \frac{1}{15}15 = \left(120 + 30 \omega\right)/(75 \omega)
|
8,043 |
\left(z + 1\right)\cdot (z + (-1)) = (-1) + z^2
|
325 |
d\times 3\times y = 3\times y\times d
|
40,649 |
3^{l + 1} = 3 \times 3^l \leq (l + 1) \times 3^l
|
-28,990 |
4\cdot \frac{1}{20}\cdot \pi = \pi/5
|
40,111 |
\cos{G} = \frac{h^2 + a^2/4 - m^2}{2 \cdot h \cdot a/2} \implies \cos{G} \cdot h \cdot a = h^2 + \frac{a^2}{4} - m \cdot m
|
9,704 |
3 + 0 \times 3 + 6 \times 2 + 6 = 21
|
13,643 |
(2 \times (5 \times t + 4)) \times (2 \times (5 \times t + 4)) + 2 \times (5 \times t + 4) = 100 \times t^2 + 160 \times t + 64 + 10 \times t + 8 = 10 \times \left(10 \times t^2 + 17 \times t + 70\right) + 2
|
-20,008 |
\frac11\cdot 1 = \frac{2 - 4\cdot a}{-4\cdot a + 2}
|
23,562 |
\frac{z^3}{2} \dfrac{1}{1 + \frac{z^2}{2}} = \frac{z^3}{z^2 + 2}
|
-20,791 |
\frac{70}{-63 \cdot p + 42 \cdot (-1)} = \frac{1}{6 \cdot (-1) - 9 \cdot p} \cdot 10 \cdot 7/7
|
-20,191 |
\frac{1}{9} \cdot (3 \cdot (-1) + x) \cdot \frac{1}{7} \cdot 7 = \dfrac{1}{63} \cdot (x \cdot 7 + 21 \cdot \left(-1\right))
|
20,653 |
(1 + 7 + 49)*(1 + 5 + 25) = 1767
|
4,825 |
(-\mu + X) \cdot \left(Y - \nu\right) = (X - \mu) \cdot Y - (-\mu + X) \cdot \nu
|
3,835 |
(-1) + \varepsilon^2 = (\varepsilon + \left(-1\right))\cdot (1 + \varepsilon)
|
7,942 |
i*x = 88 \Rightarrow 88/i = x
|
21,428 |
3^n\cdot \sin{\frac{h}{3^n}} = \tfrac{\sin{\frac{h}{3^n}}}{\dfrac{1}{3^n}}
|
19,631 |
m \cdot r_2 + r_1 \cdot m = m \cdot (r_1 + r_2)
|
17,695 |
((-1) + x^2)^2 = (1 + x)*((-1) + x)*(x + (-1))*(x + 1)
|
13,628 |
(2 + k) \cdot k \cdot (k + 1)^2 = \left(k + 3\right) \cdot (2 + k) \cdot \left(1 + k\right) \cdot k - 2 \cdot k \cdot (1 + k) \cdot (k + 2)
|
12,198 |
\cos^\frac{1}{2}(\pi) = \left(-1\right)^{\dfrac12} = (-1)^{1/2} = i
|
44,029 |
0=0+i0
|
9,997 |
x_n + x_n = 2x_n
|
301 |
(-b + a)\cdot (a^2 + a\cdot b + b^2) = a \cdot a^2 - b^3
|
-6,734 |
3/100 + 0/10 = \frac{0}{100} + 3/100
|
-11,590 |
-12 - i\cdot 9 = 0 + 12\cdot (-1) - 9\cdot i
|
24,623 |
\frac{1}{x \cdot x^{1/5}} = x^{-\frac65}
|
3,083 |
9 \cdot (-1) + (3 + 2 \cdot x)^2 = 4 \cdot x \cdot x + 12 \cdot x
|
20,109 |
3 \times (-1) + 2 = -1
|
-28,498 |
3y * y + 6y + 78 = 3(y^2 + 2y + 26) = 3(y * y + 2y + 1 + 25) = 3(\left(y + 1\right) * \left(y + 1\right) + 25) = 3((y + 1)^2 + 5^2)
|
28,078 |
(\dfrac12)^{-x} = 2^x
|
-18,946 |
8/15 = \frac{A_s}{36 \pi}*36 \pi = A_s
|
11,679 |
8\cdot a^2 = 4\cdot a\cdot 4\cdot a\cdot 1/2
|
13,062 |
8984 = 19^3 + 5 \cdot 5^2 + 10^3 + 10^3
|
16,501 |
\dfrac{1}{8} = \frac12 \cdot \frac12/2
|
27,085 |
\tan(-x) = \sin(-x)/\cos(-x) = \dfrac{1}{\cos(x)}((-1) \sin(x)) = -\tan(x)
|
-9,343 |
-27\cdot p - p^2\cdot 63 = -p\cdot p\cdot 3\cdot 3\cdot 7 - 3\cdot 3\cdot 3\cdot p
|
9,682 |
\lambda*z^2*3 = 2*z \Rightarrow \lambda = \frac{2}{z*3}
|
6,180 |
\left(\sin{z} + \cos{z}\right)^2 = 1 + 2\cdot \sin{z}\cdot \cos{z} = 1 + \sin{2\cdot z} = 1^2 = 1 \implies \sin{z\cdot 2} = 0
|
15,755 |
(-3)\times (-2) = 2 + 2 + 2 = 6
|
12,073 |
\frac12 \cdot 243 = 729/4 - \frac{729}{12}
|
14,771 |
u^2 - v^2 = (v + u)\cdot (-v + u)
|
9,740 |
5 (-1) + x = -s*2 \Rightarrow x = 5 - 2 s
|
5,837 |
\frac{1}{\beta^{-k} \frac{1}{k!}} = k! \beta^k
|
11,470 |
x/(x*2) + 2/(x*2) = (2 + x)/(2x)
|
31,324 |
\frac{1}{12 + z}\cdot (z + 7.8) = 0.8 rightarrow 9 = z
|
11,621 |
0 = y^4 + 6 \cdot y^2 + 25 = (y^2 + 5)^2 - 4 \cdot y^2 = (y^2 - 2 \cdot y + 5) \cdot (y^2 + 2 \cdot y + 5)
|
14,650 |
2^{\frac13}\cdot 2^{1/3}\cdot 2^{1/3} = 2
|
17,289 |
|u_k\cdot A^2|^2 - |u\cdot A \cdot A|^2 = (|u\cdot A \cdot A| + |A \cdot A\cdot u_k|)\cdot \left(-|A^2\cdot u| + |A \cdot A\cdot u_k|\right)
|
-20,209 |
\left(\left(-1\right)*81*z\right)/(z*9) = -9/1*9*z/(9*z)
|
-5,400 |
41.3*10^1 = 41.3*10^{1 + 0}
|
-3,355 |
\sqrt{13} + \sqrt{13}*5 = \sqrt{13}*\sqrt{25} + \sqrt{13}
|
15,647 |
4 \cdot y + z \cdot z + y^2 - z \cdot 2 = 5 \cdot \left(-1\right) + \left(z + (-1)\right)^2 + (y + 2) \cdot (y + 2)
|
17,501 |
\frac{Z}{A \cap Z} = \frac{Z}{A} = \left(A + Z\right)/A
|
5,524 |
-(2*(-1) + x) + {x \choose 2} = {(-1) + x \choose 2} + 1
|
19,240 |
(1/2 - \dfrac13)\cdot 5 = 3/2 - 2/3
|
1,490 |
\left(0 = z \cdot z - \rho^2 - 4z + 4 \Rightarrow (2(-1) + z)^2 - \rho \cdot \rho = 0\right) \Rightarrow 0 = (\rho + z + 2(-1)) (z + 2(-1) - \rho)
|
21,893 |
\left(6\times (-1) + z + 2\times (-1) + 3\times z = 0 \implies -8 = z\times 4\right) \implies -2 = z
|
-25,807 |
1*2/\left(7*6\right) = \tfrac{2}{42}
|
12,026 |
\cos(z) = \cos(z/2 + z/2) = \cos^2(\frac{z}{2}) - \sin^2\left(z/2\right) = 1 - 2\sin^2(\frac12z)
|
49,042 |
332 = 83\times 2^2
|
26,834 |
\left((2^{1/2} \cdot 25)^2 + (25 \cdot 2^{1/2})^2\right)^{1/2} = 50
|
21,464 |
-\pi/6 = (\left(-1\right)\cdot \pi)/6
|
21,385 |
\dfrac{1}{-(1 - \frac{1}{x}) + 1} = x
|
-1,933 |
-\pi/4 = -\frac{7}{12} \pi + \pi/3
|
20,717 |
q^{n + 1} \gt q^{n + 1} + (-1) = (q^n + (-1))^q \gt q^{\left(n + \left(-1\right)\right)\times q}
|
20,099 |
-2 \cdot x_2 \cdot x_1 + (x_2 + x_1)^2 = x_1 \cdot x_1 + x_2^2
|
25,630 |
\sin(w + i \cdot z) = \sin{w} \cdot \cos{i \cdot z} + \cos{w} \cdot \sin{i \cdot z} = \sin{w} \cdot \cosh{z} + i \cdot \cos{w} \cdot \sinh{z}
|
12,720 |
(f \times d)^1 = f^1 \times d^1 = f \times d
|
26,084 |
-1 + 0 + 0/2 + \tfrac04 + \frac{0}{8} = -1
|
11,329 |
\left[x,z\right] = x^Y\cdot D^2\cdot z = x^Y\cdot D^Y\cdot D\cdot z = \left(D\cdot x\right)^Y\cdot D\cdot z
|
-4,488 |
\frac{10 \cdot (-1) - 4 \cdot z}{8 \cdot (-1) + z \cdot z + z \cdot 2} = -\frac{1}{2 \cdot (-1) + z} \cdot 3 - \frac{1}{z + 4}
|
18,003 |
h_2\cdot h_1 = \frac12\cdot (\left(h_1 + h_2\right) \cdot \left(h_1 + h_2\right) - h_1^2 - h_2 \cdot h_2)
|
44,010 |
{3 \choose 0} + {3 \choose 2} = 4
|
5,423 |
1020 = 4*4*4*4*4 + 4(-1)
|
40,515 |
20\cdot 16 + 3 = 323
|
5,297 |
\frac1s(c_2 + c_1) = \dfrac{c_1}{s} + \frac{c_2}{s}
|
31,957 |
\cos\left(G + E\right) = \cos(G)*\cos\left(E\right) - \sin(G)*\sin\left(E\right)
|
30,740 |
\tfrac{1}{z \times (-\dfrac{a}{z} + 1)} = \frac{1}{-a + z}
|
-20,133 |
8*z/\left(\left(-1\right)*80*z\right) = -1/10*\left(z*\left(-8\right)\right)/\left((-8)*z\right)
|
8,487 |
x^3 + 1729 = x \cdot x \cdot x + 12^3 + 1^3 = x^3 + 10^2 \cdot 10 + 9^3
|
3,365 |
(1 + y^2 - y\cdot 4) \left(y + \left(-1\right)\right) + y\cdot (5(-1) + c) = y^3 - 5y^2 + yc + (-1)
|
3,291 |
\left(-1 = \frac{2*x*z}{z^2 + x^2} \Rightarrow 0 = (x + z)^2\right) \Rightarrow x = -z
|
25,388 |
-1 + 1 + (-1) + 1 = 0
|
33,631 |
27 > a * a * a \Rightarrow a < 3
|
-1,484 |
\frac{1}{20}36 = \frac{36*1/4}{20*\frac14} = 9/5
|
-20,511 |
\frac{1}{8\cdot p + 80\cdot (-1)}\cdot 56 = \frac{7}{p + 10\cdot (-1)}\cdot 8/8
|
27,010 |
m = m/2*2
|
3,208 |
\dfrac{132}{380} = 12/20*11/19
|
13,745 |
3^3 + 5*1^3 + 4\left(-2\right)^3 = 27 + 5 - 4*8 = 0
|
24,835 |
\frac{\mathrm{d}}{\mathrm{d}x} y * y = 2y\frac{\mathrm{d}y}{\mathrm{d}x} = 2y*0
|
-9,951 |
0.01 \cdot (-78) = -\dfrac{78}{100} = -39/50
|
9,431 |
(-y)^n + (-1)^{(-1) + n} = (-1)^{n + (-1)} + y^2 \cdot (-y)^{n + 2 \cdot (-1)}
|
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