id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
-18,254 |
\frac{1}{q^2 - 9 \cdot q + 8} \cdot \left(6 \cdot \left(-1\right) + q^2 + 5 \cdot q\right) = \frac{(q + (-1)) \cdot \left(q + 6\right)}{(8 \cdot (-1) + q) \cdot \left((-1) + q\right)}
|
-29,962 |
8y^3 + y^2 \cdot 3 + y \cdot 6 = d/dy (2y^4 + y \cdot y \cdot y + 3y^2)
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-3,351 |
5 \times 2^{1/2} = (4 + 1) \times 2^{1/2}
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6,776 |
\left(z^2 - z + 3\right) \cdot \left((-1) + z\right) \cdot (2 + z) - 5 \cdot z + 7 = z^4 + 1
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-22,366 |
(3 + l) \cdot \left(l + 6 \cdot (-1)\right) = l^2 - 3 \cdot l + 18 \cdot (-1)
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-20,198 |
10/10 (-\frac57) = -\frac{50}{70}
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-18,772 |
\frac{y*6}{3} = y*2
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6,465 |
\frac{1}{99 \times 999} \times (71700 + 71000 \times (-1) - 717 + 71 \times (-1)) = \frac{1}{99 \times 999} \times (700 + 717 \times (-1) + 71) > 0
|
17,407 |
M = M^{1/2} * M^{1/2}
|
5,008 |
(-x + 100)^2 = 10000 - x\cdot 200 + x \cdot x
|
-10,611 |
5/5*(-\frac{6}{t + 3*(-1)}) = -\frac{30}{15*\left(-1\right) + t*5}
|
13,810 |
W_0 \cdot x_0 = x_0 \cdot W_0
|
24,770 |
4 + y^4 = \left(2 + y^2 + 2 \cdot y\right) \cdot (2 + y^2 - 2 \cdot y)
|
23,027 |
g*b*c = g*b/c = \frac{1}{b*\tfrac1c}*g = g*c/b
|
-18,563 |
3\cdot r + 4\cdot (-1) = 6\cdot \left(2\cdot r + (-1)\right) = 12\cdot r + 6\cdot (-1)
|
4,301 |
\frac12*\sqrt{2} = \sqrt{\frac12}
|
8,890 |
n \cdot a = a \cdot n
|
-2,350 |
\frac{1}{20} = \frac{5}{20} - 4/20
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-11,017 |
\dfrac{130}{13} = 10
|
-23,210 |
-\frac{1}{27}4 (-1/3) = 4/81
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30,967 |
K^1 \coloneqq K
|
28,970 |
\frac{x + c}{x + d} + (-1) = \frac{1}{x + d}\cdot \left(x + c - x + d\right) = \dfrac{c - d}{x + d}
|
7,922 |
\dfrac{a \cdot \frac{1}{g}}{a \cdot \frac1g} = 1 = \frac1a \cdot a
|
-2,206 |
\frac{5}{11} = 9/11 - 4/11
|
-16,914 |
5 = 5 \times 3 \times q + 5 \times \left(-7\right) = 15 \times q - 35 = 15 \times q + 35 \times (-1)
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-23,066 |
-32/3 = -8*\frac13*4
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-4,512 |
\frac{20 + \xi\cdot 2}{12\cdot (-1) + \xi^2 - \xi} = -\frac{2}{\xi + 3} + \frac{1}{\xi + 4\cdot (-1)}\cdot 4
|
4,665 |
\sin(2\cdot A) + \sin(2\cdot B) + 2\cdot \sin(A + B) = ... = 4\cdot \sin(A + B)\cdot \sin^2((A - B)/2)
|
-518 |
e^{\dfrac12 \cdot 3 \cdot i \cdot \pi \cdot 10} = (e^{3 \cdot \pi \cdot i/2})^{10}
|
10,420 |
\left(-1\right) + 5^{l \cdot 2} = (1 + 5^l) \cdot (5^l + (-1))
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-15,788 |
-47/10 = \dfrac{7}{10} - 9/10 \cdot 6
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7,249 |
13^4*7^2*3^2*17^5 = \left(3*7*13^2\right) * \left(3*7*13^2\right)*17^5
|
7,670 |
k + 2 \cdot (-1) - i + 1 = k + 2 \cdot (-1) - (-1) + i
|
6,884 |
\sin(\pi + f) = -\sin\left(f\right)
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-22,213 |
l \cdot l - 11\cdot l + 18 = (9\cdot \left(-1\right) + l)\cdot (2\cdot \left(-1\right) + l)
|
41,412 |
\binom{10}{8}\cdot \binom{2}{2} = 45
|
8,512 |
y*\left(f + h\right) = yf + hy
|
-20,533 |
\frac{1}{1}\cdot 4\cdot \frac{1}{5 + 7\cdot y}\cdot (7\cdot y + 5) = \dfrac{1}{5 + 7\cdot y}\cdot (20 + 28\cdot y)
|
32,607 |
Z \times x = x \times Z
|
37,914 |
2\times 60 - 109 = 11
|
-22,044 |
\dfrac{1}{4}\cdot 9 = 27/12
|
32,653 |
a \cdot f = \frac{1}{f \cdot a} = f \cdot a
|
41,164 |
3630 = 480 + 180 + 360 + 720 + 90 + 1080 + 360 + 360
|
-7,077 |
3/13\cdot 4/14 = \frac{6}{91}
|
35,281 |
5 \cdot \frac{16}{36} - 5 \cdot 20/36 = -20/36 = -\frac{5}{9}
|
1,970 |
X B = X B
|
3,389 |
13/12 = 1/2 + \frac14 + \frac{1}{3}
|
-9,070 |
99.6/100 = 99.6\%
|
-6,260 |
\dfrac{4}{(2\cdot (-1) + h)\cdot 2} = \frac{1}{4\cdot (-1) + 2\cdot h}\cdot 4
|
31,957 |
\cos(B + A) = -\sin{B}\cdot \sin{A} + \cos{B}\cdot \cos{A}
|
2,106 |
\sin(\theta) \cdot \cos(\varphi) + \cos(\theta) \cdot \sin(\varphi) = \sin\left(\varphi + \theta\right)
|
33,070 |
(x + 1)^3 = x \cdot x \cdot x + 3 \cdot x^2 + 3 \cdot x + 1 = x^3 + 3 \cdot x + 3 \cdot x^2 + 1 \gt 3 \cdot x^2 + 1
|
6,559 |
\tan^{-1}(0) + \tan^{-1}(0^2 + (-1)) = 0 + \tan^{-1}(-1) = \left((-1)\cdot \pi\right)/4
|
-2,457 |
\sqrt{5}\cdot \left(5 + 3\cdot (-1)\right) = 2\cdot \sqrt{5}
|
-20,658 |
-7/3\cdot \frac{1}{p + 10\cdot (-1)}\cdot (p + 10\cdot \left(-1\right)) = \frac{-7\cdot p + 70}{p\cdot 3 + 30\cdot \left(-1\right)}
|
-17,472 |
18\cdot (-1) + 20 = 2
|
-28,770 |
\frac12 + \frac{1}{2*z + 6} = \tfrac{4 + z}{2*z + 6}
|
28,700 |
\frac{12}{26} = \dfrac{6}{13}
|
-6,011 |
\frac{3}{(d + 1) \cdot 3} = \frac{1}{d \cdot 3 + 3} \cdot 3
|
-654 |
-\pi \cdot 16 + \pi \cdot \frac{33}{2} = \pi/2
|
11,275 |
r^nr^m = r^{n+m} \in IJ
|
13,795 |
\frac{1}{L + x} = x - L + L^2 - L^3 + \ldots
|
4,559 |
\sin(z_2 + z_1) = \cos{z_1} \sin{z_2} + \sin{z_1} \cos{z_2}
|
-21,021 |
\frac{1}{50*n}*(-5*n + 25*(-1)) = 5/5*(5*\left(-1\right) - n)/\left(n*10\right)
|
48,033 |
\left((a + b)^2 = a \cdot b \implies a^2 + 2 \cdot a \cdot b + b \cdot b = b \cdot a\right) \implies b \cdot b + a \cdot a + a \cdot b = 0
|
16,609 |
\tfrac{(1 + 1 + 1)!}{1! \cdot 1! \cdot 1!} = 3! = 6
|
21,497 |
c + y \cdot f = 0 \Rightarrow y = ((-1) \cdot c)/f
|
17,213 |
h^{z + c} = h^c \cdot h^z
|
15,666 |
(12 (-1) + x^2 + 5x) (5\left(-1\right) + x) = x^3 - 37 x + 60
|
10,496 |
14.5 = \cos{z} + 5 \Rightarrow \cos{z} = 9.5
|
-4,128 |
\frac{5}{12} = \frac{1}{12} \times 5
|
-12,684 |
38 = \frac15*190
|
30,505 |
f\frac{1}{b}/\left(f\tfrac{1}{b}\right) = 1 = fb/b/f
|
-1,419 |
\dfrac{1}{9\cdot \dfrac17\cdot 8} = \frac{1}{9}\cdot \frac{7}{8}
|
-10,391 |
-12 = 5 + 16 \cdot d + 20 \cdot (-1) = 16 \cdot d + 15 \cdot (-1)
|
28,045 |
0.5441 = 0.08 \cdot 0.49 + \left((-1) \cdot 0.01 + 1\right) \cdot 0.51
|
-18,383 |
\frac{1}{(x + 4(-1)) (x + 4(-1))}(x + 4(-1)) x = \tfrac{1}{16 + x * x - 8x}(x * x - x*4)
|
13,288 |
-(3*\left(-1\right) + x * x)^2 + x^4 - 6*x^2 + 4*x + 3*\left(-1\right) = 12*(-1) + 4*x
|
13,925 |
-e^{x*3} + \frac{\mathrm{d}15}{\mathrm{d}x} = -3*e^{3*x}
|
-30,558 |
-\frac{1}{32} \cdot 256 = 32/(-4) = -\dfrac{1}{\frac12} \cdot 4 = -8
|
14,970 |
y \cdot 142 = 22 y + 120 y
|
-26,401 |
z^n\times z^m = z^{n + m}
|
-23,808 |
\frac{1}{7 + 2} \cdot 45 = 45/9 = \frac19 \cdot 45 = 5
|
28,319 |
1 + z + \cdots z^{K_k} = \frac{1}{1 - z} (1 - z^{K_k + 1})
|
19,276 |
πR*2 πr * r = π * π Rr^2*2
|
-18,980 |
7/24 = \frac{1}{4\cdot \pi}\cdot A_s\cdot 4\cdot \pi = A_s
|
-6,708 |
8/10 + \frac{1}{100}\cdot 4 = 4/100 + \frac{80}{100}
|
-28,800 |
\frac{π \cdot 2}{\dfrac{1}{29.5} \cdot π \cdot 2} = 29.5
|
6,069 |
1=B+C \implies C=1-B
|
-19,301 |
\dfrac{1}{5} \div \dfrac{9}{5} = \dfrac{1}{5} \times \dfrac{5}{9}
|
8,636 |
a*H*n*H/\left(a*H\right) = n*H = a*\frac1a*n*H
|
8,179 |
1 = z y^n \Rightarrow y^{-n} = z
|
2,610 |
65 = \frac12 \cdot (1^7 + 1^7 + 2^7)
|
24,863 |
1 - y = 1 - y^2 = (1 - y)*(1 + y)
|
4,485 |
\frac{1}{4}\cdot 3 = \frac{3\cdot \frac{1}{10}}{1/10 + 3/10}
|
16,332 |
-2 * 2 * 2 + z^3 = (2^2 + z^2 + z*2)*(z + 2*(-1))
|
11,988 |
(-1) + n*2 = 2\left(n + (-1)\right) + 1
|
-6,801 |
12 \times 10 \times 5 = 600
|
-15,810 |
37/10 = -\frac{1}{10} \cdot 8 + 9/10 \cdot 5
|
25,843 |
\pi/2 + \frac{\pi}{2} + \frac{\pi}{3} \cdot 2 = \pi \cdot 5/3
|
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