id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-12,252 |
17/18 = \frac{x}{18\cdot π}\cdot 18\cdot π = x
|
12,587 |
5 \cdot 0 + 4 \cdot 2 + 3 \cdot 3 + 2 \cdot 7 + 15 = 46
|
-9,321 |
-36 \cdot m + 42 = 2 \cdot 3 \cdot 7 - 2 \cdot 2 \cdot 3 \cdot 3 \cdot m
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-233 |
\binom{7}{5} = \frac{7!}{(7 + 5\cdot (-1))!\cdot 5!}
|
54,186 |
25 = 5 + 10 + 10
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27,140 |
|a - x| + |x - c| = -(a - x) + x - c = -a + 2\cdot x - c
|
31,301 |
378 = \frac{756}{2}1
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-12,127 |
1/2 = \frac{1}{14 \times \pi} \times x \times 14 \times \pi = x
|
4,450 |
(-1) + 6\cdot k^2 + k = (3\cdot k + (-1))\cdot (2\cdot k + 1)
|
190 |
\cos{\pi/2} + (\pi/2)^3 \cdot \dfrac{8}{\pi^3} + \pi/2 \cdot 2 = 1 + \pi
|
-5,936 |
\frac{1}{36*\left(-1\right) + l * l - 5*l}*4 = \frac{1}{(4 + l)*\left(l + 9*(-1)\right)}*4
|
5,656 |
11 \cdot 9 = \left(-1\right) + 10^2
|
26,470 |
\sqrt{7 - i*24} = z \Rightarrow z^2 = 7 - i*24
|
16,928 |
(a + b)/\left(a b\right) = 1/a + 1/b
|
14,727 |
z^6 + z^4 + z^3 - z^2 + (-1) = (z^4 + z \cdot z^2 + (-1)) \cdot (z^2 - z + 2) - z^2 \cdot z - z + 1
|
-4,605 |
\frac{1}{20\cdot \left(-1\right) + z \cdot z - z}\cdot \left(3\cdot z + 30\right) = \dfrac{5}{5\cdot \left(-1\right) + z} - \tfrac{1}{z + 4}\cdot 2
|
48,850 |
2\times \sqrt{|\varepsilon|} = |\sqrt{\varepsilon} - \sqrt{\varepsilon + x} + \sqrt{\varepsilon} + \sqrt{\varepsilon + x}| \leq |\sqrt{\varepsilon + x} - \sqrt{\varepsilon}| + |\sqrt{\varepsilon + x} + \sqrt{\varepsilon}|
|
1,111 |
z^4 + 1 = (1 + z^2 - z\cdot \sqrt{2})\cdot (z^2 + z\cdot \sqrt{2} + 1)
|
25 |
\left(n + (-1)\right)!\times (n + (-1) + 1) = \left(n + (-1)\right)!\times n = n!
|
-5,619 |
\dfrac{2}{(y + 6 \left(-1\right)) (5 + y)} = \tfrac{2}{30 (-1) + y^2 - y}
|
22,641 |
x * x * x + p^3 + d^3 - 3*x*p*d = (d + x + p)*(x^2 + p * p + d^2 - p*x - x*d - d*p)
|
41,758 |
\sin \pi=0
|
-20,682 |
\frac{1}{-16\cdot q + 32}\cdot (-q\cdot 2 + 4) = \frac{1}{8}\cdot 1
|
6,491 |
17^2 + 7 \cdot 7 + 5^2 = 4 \cdot 4 + 1^2 + 15^2 + 11^2
|
-11,122 |
\left(y + 2\left(-1\right)\right)^2 + b = \left(y + 2\left(-1\right)\right) (y + 2\left(-1\right)) + b = y^2 - 4y + 4 + b
|
26,584 |
(-1) + u^3 = (1 + u^2 + u)*((-1) + u)
|
16,669 |
(-b + a) \times (a^2 + a \times b + b^2) = -b^3 + a \times a^2
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-7,782 |
\frac{i\cdot 20 + 10}{4 + i\cdot 2}\cdot \frac{-2\cdot i + 4}{4 - 2\cdot i} = \frac{10 + 20\cdot i}{i\cdot 2 + 4}
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-554 |
(e^{\frac{13*\pi*i}{12}})^{13} = e^{\frac{\pi*i}{12}*13*13}
|
30,544 |
\cos(\sin^{-1}(\xi)) = \sqrt{-\xi^2 + 1}
|
1,981 |
-h_2^2 + h_1^2 = (-h_2 + h_1) \cdot \left(h_1 + h_2\right)
|
-2,436 |
\sqrt{16*6} + \sqrt{6} + \sqrt{4*6} = \sqrt{6} + \sqrt{24} + \sqrt{96}
|
25,519 |
X^4 - 4\cdot X^3 - X^2\cdot 19 - X\cdot 4 + 1 = \left(X^2 + 3\cdot X + 1\right)\cdot \left(1 + X \cdot X - X\cdot 7\right)
|
2,930 |
y^3 + 8(-1) = (y + 2(-1)) (4 + y^2 + y*2)
|
24,093 |
\frac{2}{-p^2 + 1} = \frac{1}{-p + 1} + \frac{1}{p + 1}
|
-22,306 |
(y + 6 \cdot (-1)) \cdot (y + 5 \cdot (-1)) = 30 + y^2 - 11 \cdot y
|
19,924 |
0 + (j - i + (-1))*(-D_p^2 + p) + p - D_p^2 = (-D_p^2 + p)*(-i + j)
|
25,154 |
\frac{1}{2009}\cdot \left(1544 - \frac{1}{2}\right) = \frac{63}{82}
|
20,349 |
K + e^D = \frac{1}{x \cdot e^{-D}} rightarrow 1/x = \frac{1}{e^D} \cdot \left(e^D + K\right)
|
42 |
-90 \cdot n \cdot n = -(6 \cdot 20 + 30 \cdot \left(-1\right)) \cdot n \cdot n
|
3,783 |
341 = 10^0 + 10 \cdot 10\cdot 3 + 4\cdot 10^1
|
-2,076 |
π \cdot \frac{3}{4} + \dfrac13 \cdot π = \frac{1}{12} \cdot 13 \cdot π
|
-22,382 |
y \cdot y - y\cdot 8 + 20\cdot \left(-1\right) = \left(y + 2\right)\cdot (y + 10\cdot (-1))
|
12,718 |
((-1) + y) (y + 4) = 4(-1) + y^2 + 3y
|
34,110 |
GG = G^2
|
35,732 |
2^{n + 1} = 2\cdot 2^n = 2^n + 2^n
|
34,595 |
X^k*C = C*X^k
|
-23,451 |
1/5 \cdot 2/3 = \dfrac{2}{15}
|
-23,821 |
\frac{1}{2 + 8}\cdot 20 = 20/10 = \frac{20}{10} = 2
|
5,743 |
\left(\frac43 + 2\right)/6 = \frac59
|
35,502 |
z^2 z = z^2 z
|
11,474 |
v = x^2 \cdot \alpha \Rightarrow x = \sqrt{v/\alpha}
|
10,894 |
x/f = \frac1d*h \Rightarrow d*x = f*h
|
-20,452 |
-\frac{70}{56\cdot y + 49\cdot (-1)} = \dfrac77\cdot (-\tfrac{10}{y\cdot 8 + 7\cdot (-1)})
|
17,682 |
\left(-b + a\right) \times \left(a + b\right) = -b^2 + a^2
|
30,681 |
2\times 2 \times 3 \times 3 \times 5 =180
|
-20,241 |
-\tfrac{1}{6}*\frac{1}{-5*x + 5*\left(-1\right)}*(5*\left(-1\right) - 5*x) = \frac{5 + 5*x}{30*(-1) - 30*x}
|
-5,620 |
\frac{3}{(b + 6)\cdot (8\cdot \left(-1\right) + b)} = \frac{3}{b^2 - b\cdot 2 + 48\cdot (-1)}
|
-30,238 |
\frac{1}{z + (-1)}*(z^2 - 2*z + 1) = \frac{1}{z + (-1)}*(z + (-1))^2 = z + \left(-1\right)
|
-20,610 |
\tfrac{1}{28 - x*20}(x*45 + 63 (-1)) = -9/4 \frac{7 - 5x}{-x*5 + 7}
|
-29,669 |
\frac{\mathrm{d}}{\mathrm{d}z} (-2\cdot z^5 - z^3\cdot 3 + 1) = -10\cdot z^4 - 9\cdot z^2
|
-16,436 |
10*\sqrt{16*11} = 10*\sqrt{176}
|
23,120 |
ln(e^x)=xlog_e e=x
|
22,916 |
575757 = \frac{39!}{(39 + 5(-1))!*5!}
|
-4,564 |
\dfrac{1}{2 \cdot (-1) + z^2 - z} \cdot (7 \cdot (-1) - 4 \cdot z) = -\dfrac{1}{2 \cdot (-1) + z} \cdot 5 + \dfrac{1}{1 + z}
|
17,762 |
j! = j*\left(j + (-1)\right)! = j*\left(j + \left(-1\right)\right)*(j + 2*(-1))!
|
-10,299 |
5/5 \left(-\frac{1}{3t + 3(-1)}\right) = -\frac{5}{15 (-1) + t*15}
|
-2,309 |
-6/17 + \frac{7}{17} = 1/17
|
6,186 |
a^{3/2}/(\tfrac{1}{a}) = a^{3/2} a = a^{\frac{5}{2}}
|
16,490 |
\frac{1}{y}\cdot z = 2\cdot z/(y\cdot 2)
|
14,840 |
255253 = 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 + 2 \cdot (-1)
|
24,257 |
\frac{1}{256}\cdot 15 = 15\cdot 1/16/16
|
-10,334 |
\dfrac{4}{4}*8/(2q) = 32/(q*8)
|
-20,474 |
\tfrac18\cdot 1 = \frac{1}{8\cdot q + 48}\cdot \left(6 + q\right)
|
1,072 |
\frac{(-i*h + g)^{-1}*(-h*i + g)}{g + i*h} = \left(h*i + g\right)^{-1}
|
28,851 |
\frac{\mathrm{d}}{\mathrm{d}x} \tan^3(x) - 3\tan(x) + x*3 = \tan^4(x)*3
|
9,546 |
G\cdot G = G\cdot (0 + G)
|
32,058 |
24 > -3\cdot z rightarrow 8 \gt -z
|
-13,020 |
\frac{9}{21} = \tfrac37
|
12,992 |
F^2 + A^2 + A \cdot F + A \cdot F = (A + F)^2
|
-5,774 |
\frac{5}{4\cdot (y + 6)} = \frac{5}{4\cdot y + 24}
|
30,687 |
(3 - 5^{1 / 2})/2 = 3/2 - \frac{1}{2} 5^{\frac{1}{2}}
|
18,703 |
m*(1 + n) = m + m*n
|
8,785 |
z\times x\times y = z\times y\times x
|
50,792 |
6^4 =1296
|
31,734 |
-q_l + q \lt x \implies q_l \gt q - x
|
9,231 |
1 + \frac{1}{2}\times (1 - \sqrt{5}) = ((1 - \sqrt{5})/2)^2
|
29,863 |
\sin^{-1}(\sin(y)) = \sin^{-1}\left(\sin(π - y)\right) = π - y
|
-16,516 |
4 \cdot \sqrt{16} \cdot \sqrt{3} = 4 \cdot 4 \cdot \sqrt{3} = 16 \cdot \sqrt{3}
|
-20,858 |
-8/9 \cdot (-5/(-5)) = \dfrac{40}{-45}
|
9,247 |
(\dfrac{1}{3}\cdot 2)^6 = 64/729
|
-25,487 |
d/dy \left(-\cos(y) + y^3\right) = 3 \cdot y^2 + \sin(y)
|
125 |
(\alpha \cdot c \cdot x)^2 = \alpha \cdot \alpha \cdot c^2 \cdot x^2
|
16,142 |
\sin(2*w) = -\sin(C)\Longrightarrow 2*w = \sin^{-1}(-\sin\left(C\right))
|
5,180 |
1 + y^4 + y^2 = (1 + y^2 + y) (y^2 - y + 1)
|
-20,332 |
2/2 \cdot \frac{1}{-4} \cdot \left(5 \cdot (-1) + y \cdot 5\right) = \frac{1}{-8} \cdot (10 \cdot (-1) + y \cdot 10)
|
2,284 |
\dfrac{\sin(\pi z/2)}{z} = \frac{\sin(\dfrac{z}{2}\pi)}{\frac{1}{2} \pi z} \frac{\pi}{2}
|
29,547 |
x \cdot h = h \cdot x \cdot h/h
|
24,762 |
(1 + \sin(A))\cdot \left(-\sin\left(A\right) + 1\right) = \cos^2(A)
|
7,952 |
1 - x_1 + x_2 + x_1 x_2 = (-x_2 + 1) (1 - x_1)
|
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