id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
36,502 |
1 = \frac12 + 1/3 + 1/9 + 1/18
|
-18,259 |
\frac{1}{x^2 - x*2 + 63 \left(-1\right)}(x * x + x*7) = \dfrac{x*(x + 7)}{(x + 7) (x + 9(-1))}
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18,598 |
5 \cdot \pi/12 = \pi/4 + \frac{1}{6} \cdot \pi
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13,069 |
f^3 - 6*f^2 + 11*f + 6*(-1) = (f + (-1))*(f * f - 5*f + 6) = (f + \left(-1\right))*(f + 2*(-1))*\left(f + 3*(-1)\right)
|
11,242 |
9/48 + \dfrac{3}{54} = 3/16 + 1/18 = \dots
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-15,125 |
\frac{n^5}{\frac{1}{y^6} \cdot \dfrac{1}{n^{10}}} = \frac{n^5}{\frac{1}{y^6 \cdot n^{10}}}
|
-725 |
\pi \cdot \frac{49}{12} - 4 \cdot \pi = \pi/12
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-9,201 |
15 p + 45 = 3 \cdot 3 \cdot 5 + 3 \cdot 5 p
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-8,036 |
\dfrac{27 - 5 \cdot i}{5 - i \cdot 2} \cdot \dfrac{5 + i \cdot 2}{i \cdot 2 + 5} = \frac{27 - 5 \cdot i}{-i \cdot 2 + 5}
|
-9,285 |
2\cdot 2\cdot 2\cdot 5 - 2\cdot 2\cdot 2\cdot s = -8\cdot s + 40
|
450 |
z^6 + 1 = (z^2 + 1) \left(z^4 - z^2 + 1\right) = (z z + 1) ((z + 1)^2 - z z)
|
-21,700 |
-9/8 = -\frac{1}{8}*9
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-1,247 |
\frac{30}{35} = \frac{6}{35*\frac15}*1 = 6/7
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-10,816 |
\dfrac{1}{12} 48 = 4
|
15,335 |
( x, z, p)\cdot ( x', S, Z) \coloneqq \left( x' + x, z + S, p + Z + \left(-x'\cdot z + x\cdot S\right)/2\right)
|
27,319 |
-q + p - r = -(r + q) + p
|
18,983 |
z/(c_2) + \tfrac{1}{c_1}\cdot x = \tfrac{1}{c_2\cdot c_1}\cdot (c_2\cdot x + z\cdot c_1)
|
35,182 |
\frac{\mathrm{d}D}{\mathrm{d}x} = \frac{\mathrm{d}D}{\mathrm{d}x}
|
27,242 |
\dfrac{1}{3}\cdot (2\cdot a + 2\cdot d + y) = \frac15\cdot (3\cdot a + 4\cdot y) = (2\cdot a + d + 2\cdot y)/3
|
-6,295 |
\frac{1}{(2\cdot (-1) + n)\cdot 4} = \frac{1}{n\cdot 4 + 8\cdot \left(-1\right)}
|
14,202 |
q^2 - 2 \cdot q + 1 = (\left(-1\right) + q) \cdot (\left(-1\right) + q)
|
25,876 |
\frac{1}{2}(z_n + \frac{2}{z_n}) = z_n - \left(z_n^2 + 2(-1)\right)/(2z_n)
|
-2,365 |
(-6)^2 = \left(-6\right) \cdot \left(-6\right) = 36
|
24,395 |
x^2 \cdot B^2 + 6 \cdot x \cdot B + 9 \cdot (-1) = (x \cdot B)^2 + 5 \cdot x \cdot B + 9 \cdot (-1) = (x \cdot B + 2.5)^2 - 15.25
|
-13,130 |
134.4/4 = 33.6
|
-1,897 |
5/4 \pi = \dfrac167 \pi + \dfrac{\pi}{12}
|
2,169 |
A \cdot D \cdot t = t \cdot D \cdot A
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-2,321 |
\frac{2}{14} = -2/14 + 4/14
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-7,957 |
\frac{-45 - i \cdot 5}{5 \cdot i + 4} = \frac{-5 \cdot i + 4}{4 - 5 \cdot i} \cdot \frac{-45 - 5 \cdot i}{4 + i \cdot 5}
|
2,130 |
(2*(-1) + d)*(\left(-1\right) + d) = d^2 - d*3 + 2
|
-1,668 |
-\pi \cdot \frac{2}{3} + 3/4 \cdot \pi = \dfrac{\pi}{12}
|
22,682 |
d + g + x = x + d + g
|
5,619 |
\left(-s + x\right)\cdot \left(x - r\right) = s\cdot r + x \cdot x - (r + s)\cdot x
|
20,529 |
x = z^2 \implies 2z = \frac{\mathrm{d}x}{\mathrm{d}z}
|
-9,286 |
-49\times m + 21 = -m\times 7\times 7 + 3\times 7
|
1,172 |
k^2 = ((k + 1) \cdot (k + 1) \cdot (k + 1) - k \cdot k \cdot k)/3 - k - \dfrac13
|
-2,350 |
\frac{1}{20} = -\dfrac{4}{20} + \frac{1}{20} \cdot 5
|
15,024 |
(2 - x)/3 = -\left(1 + x\right)/3 + 1
|
27,808 |
-(y + (-1)) - 1 = -y
|
-19,997 |
\frac{72*(-1) - 54*s}{12*s + 16} = \frac{8 + 6*s}{6*s + 8}*(-9/2)
|
-13,021 |
10/18 = \frac59
|
538 |
i \cdot \frac{dx}{dx} = \frac{dx}{dy}
|
26,267 |
0 = \left(h*q - q\right)*h = h*q*h - q*h
|
-23,162 |
\frac{1}{2}\cdot \left((-1)\cdot 1/2\right) = -1/4
|
14,111 |
B*D*v = D*B*v
|
-6,438 |
\dfrac{1}{20*(-1) + 2*x} = \frac{1}{2*(10*(-1) + x)}
|
11,284 |
C^4 + C^2 + 1 = (C^2 + 1)^2 + C^2 = \left(C^2 + C + 1\right)^2
|
6,978 |
(-(-g + b)^2 + (b + g)^2)/4 = g\times b
|
-26,287 |
2 = C \times e^{(-3) \times 0} = C
|
35,185 |
3 = \frac{2}{2} + \frac42
|
4,200 |
0 + 0 + 0 = 1 + (-1) + ((-1) + 1)\cdot ...
|
12,813 |
\sqrt{x \times x} = \left(x^2\right)^{\frac{1}{2}} = x^{2/2} = x
|
22,378 |
X \cdot c \cdot E = E \cdot X \cdot c
|
6,308 |
0 = x^2*3 - 13*x + 14 \implies 0 = (7*(-1) + 3*x)*(2*\left(-1\right) + x)
|
5,392 |
\dfrac{1}{2^n} \cdot n! \geq \frac{n^{n/2}}{2^{\frac{1}{2} \cdot 3 \cdot n}} = (\frac{n}{2^3})^{\frac{n}{2}} = \left(n/8\right)^{n/2}
|
-4,773 |
\frac{5}{1 + z} - \frac{3}{2(-1) + z} = \tfrac{13 (-1) + 2z}{2(-1) + z^2 - z}
|
4,703 |
0 = y_3 - y_4*2\Longrightarrow y_3 = 2y_4
|
4,258 |
2 + 2*\sqrt{-2} = 0 + \sqrt{-2}*(2 - \sqrt{-2})
|
15,943 |
25 - 2*\left(--\frac23*3*2 + 4\right) = 9
|
13,552 |
(1 + 2k)/2 = 1/2 + k
|
5,395 |
4*(-1) + j_1*10 + 3 = 7*j_2 \Rightarrow 10*j_1 - 7*j_2 = 1
|
37,755 |
(2 (-1) + 3)^2 = 1
|
-26,159 |
-9 \cdot \cos{6 \cdot π} - -9 \cdot \cos{\tfrac{11}{2} \cdot π} = -9 + 0 \cdot (-1) = -9
|
23,878 |
h_x^3 = h_x h_x h_x
|
13,190 |
BE^2 = 16 + 9 + 6(-1) = 19 \implies BE = \sqrt{19}
|
7,418 |
x^2 + 4 x + 3 = (x + 1) \left(x + 3\right)
|
34,616 |
1 + \cos{z} = 1 + \cos{2 \cdot \frac{z}{2}} = 2 \cdot \cos^2{\frac{z}{2}}
|
29,200 |
\frac{q \cdot q}{\pi}\cdot \pi = q^2
|
24,324 |
\dfrac{18}{(1 + 5 + 4\cdot (-1))\cdot 3} = 3
|
22,483 |
b \cdot (-h) = -h \cdot b
|
-10,569 |
3/(75\cdot y) = \frac13\cdot 3/(y\cdot 25)
|
31,046 |
\left|{E_1 \cdot \cdots \cdot E_m}\right| = \left|{E_1}\right| \cdot \cdots \cdot \left|{E_m}\right|
|
17,279 |
\left(2 + y\right) \cdot (4 \cdot (-1) + y^2 - 2 \cdot y) = y^3 - 8 \cdot y + 8 \cdot (-1)
|
-15,597 |
\frac{a}{\frac{1}{\tfrac{1}{r^6} \frac{1}{a^6}}} 1/r = \dfrac{\frac1r}{a^6 r^6} a
|
40,197 |
550 + 55 \cdot \left(-1\right) = 495 < 500
|
23,330 |
\frac{l!}{(-k + l)! \cdot k!} = \binom{l}{k}
|
-30,970 |
t \cdot 60 = 60 t
|
9,894 |
(2*k)^2 - 2*2*k + 7 = 4*k^2 - 4*k + 7 = 2*(2*k^2 - 2*k) + 7
|
301 |
a^3 - b^3 = (-b + a) (a^2 + a b + b^2)
|
14,186 |
x + b = 2 \cdot b + x - b
|
13,437 |
\frac{1}{k + n} = \frac{1}{1 + n + (-1) + k}
|
1,724 |
2*( q, z) = \left( q, z\right) + ( q, z) = ( 2*q, 2*z)
|
12,847 |
\frac{\dfrac16}{6}\cdot 1\cdot 5/6 = \frac{5}{216} = 0.023
|
29,216 |
\dfrac{-7 + (-1)}{(1 - 7)^3} = \frac{1}{27}
|
21,651 |
\frac{1}{z} = az/a = a^2 \cdot \frac{1}{za^2}
|
3,324 |
(1 + x) (1 + x) (x + 1)^{n + 2 (-1)} = \left(x + 1\right)^n
|
28,317 |
\frac{1}{1 - \dfrac23} = 3
|
-7,159 |
\dfrac{1}{78} \cdot 5 = 5/12 \cdot \frac{1}{13} \cdot 2
|
27,344 |
\cos(\pi/4) = \sin(\pi/4) = \dfrac{1}{\sqrt{2}}
|
25,124 |
24 = \tfrac{1}{2} \cdot 48
|
16,214 |
\sin{c} \times \cos{a} + \sin{a} \times \cos{c} = \sin\left(c + a\right)
|
4,783 |
z^2 + 1 = z^2 + 2 \cdot z + 1 = (z + 1)^2
|
28,449 |
I + H = I + H
|
-2,027 |
\frac{1}{12}\cdot 19\cdot \pi + \pi\cdot 3/4 = \pi\cdot \frac13\cdot 7
|
-20,291 |
\dfrac{-2\cdot a + 6}{6 - 2\cdot a}\cdot \dfrac53 = \frac{1}{-a\cdot 6 + 18}\cdot (-10\cdot a + 30)
|
1,238 |
d \cdot a = \frac{d}{a} = a^3 \cdot d
|
-30,858 |
y + 3 = \tfrac{1}{y * y * y - y^2}*(-3*y^2 + y^4 + 2*y^3)
|
1,242 |
x \cdot \left(n' + k\right) = x \cdot n' + k \cdot x
|
38,263 |
(a^t)^l = \left(a^l\right)^t = a^{t l}
|
-22,213 |
(k + 2\cdot (-1))\cdot (9\cdot (-1) + k) = k^2 - 11\cdot k + 18
|
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