id
int64 -30,985
55.9k
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stringlengths 5
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|---|---|
30,028 |
(\left(b + 1\right)^2 - 1^2)*4.9/b = (4.9*(b + 1)^2 - 4.9*1^2)/b
|
13,011 |
(X + T)*\left(X + T\right)^i = (X + T)*(X^i + i*X^{i + (-1)}*T) = X^{i + 1} + i*X^i*T + T*X^i + i*T*X^{i + (-1)}*T
|
-7,263 |
\frac{1}{91} \cdot 12 = 6/14 \cdot 4/13
|
11,591 |
(1 + h)\cdot (1 + g) + (-1) = g + h + g\cdot h
|
21,494 |
\frac{4}{3*1/6}*\frac15 = \dfrac15*8 = 1.6
|
11,428 |
b*h*a_k = b*a_k*h
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2,976 |
1 = \left(c^2 + c + 1\right)\cdot (k\cdot c^2 + l\cdot c + m) = k\cdot c^4 + (k + l)\cdot c^3 + (k + l + m)\cdot c^2 + (l + m)\cdot c + m
|
-207 |
\frac{1}{(7 + 4(-1))!}7! = 7*6*5*4
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-3,263 |
-\sqrt{2} + \sqrt{4} \cdot \sqrt{2} = -\sqrt{2} + \sqrt{2} \cdot 2
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30,980 |
\pi/4 + \pi/6 = \pi*5/12
|
334 |
\frac{x^p + (-1)}{\left(-1\right) + x} = 1 + x + \cdots + x^p
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30,368 |
-1 = (p + (-1)) \cdot (1 + p + p^2 + \dots) = p + (-1) + (p + (-1)) \cdot p + (p + (-1)) \cdot p^2 + \dots
|
-560 |
(e^{\dfrac{\pi}{12}\cdot i})^3 = e^{3\cdot \pi\cdot i/12}
|
-18,388 |
\tfrac{1}{(x + 3) \times (3 \times (-1) + x)} \times x \times (x + 3) = \frac{1}{x^2 + 9 \times (-1)} \times (x \times 3 + x \times x)
|
31,661 |
10 + 3^{1/2}\cdot 6 = 10 + 108^{1/2}
|
8,692 |
\tfrac{1}{-q + 1} \cdot (-q^{n + 1} + 1) = 1 + q + q \cdot q + \ldots + q^n
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13,160 |
4 + r^4 = (r^2 + 2\cdot r + 2)\cdot (r \cdot r - 2\cdot r + 2)
|
29,204 |
1 + (h + (-1)) \cdot (c + (-1)) = c \cdot h - c + h + 2
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15,419 |
(-q + x \cdot m + d)^2 = \left(-q + x \cdot m + d\right) \cdot \left(m \cdot x + d - q\right)
|
6,674 |
\left(a + 2 = |2\cdot a - a\cdot i| \implies 2 + a\cdot \sqrt{5} + a = 0\right) \implies -\dfrac{2}{1 + \sqrt{5}} = a
|
23,021 |
|3*\pi*2/\left(3*\pi\right) + 5| = 2 + 5 = 7
|
-28,768 |
\frac{1}{z^3 + 3}(z^6 + 2z^4 + z*6 + 9(-1)) = z^3 + z*2 + 3(-1)
|
12,932 |
n \cdot 2 \cdot c = c \cdot n \cdot 2
|
33,357 |
-a=0-a=(a+a)-a=a
|
35,450 |
\int |f|\,dx = \int |f|\,dx
|
-4,232 |
40/24 \cdot \frac{1}{r^5} \cdot r^2 \cdot r = \dfrac{r^3 \cdot 40}{r^5 \cdot 24}
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41,393 |
2 \cdot m = m + m \geq m
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11,376 |
\tfrac{1}{y}(e^y + (-1)) = z \Rightarrow 1 + zy = e^y
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-5,223 |
10^{-2 - -3}\cdot 3.2 = 10^1\cdot 3.2
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-20,698 |
\dfrac{1}{9} \times \dfrac{a - 1}{a - 1} = \dfrac{a - 1}{9a - 9}
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22,677 |
x_l*(1 + \alpha) = x_l + \alpha*x_l
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42,962 |
312 = 12*6 + 20*12
|
-30,759 |
9\cdot y + 6\cdot (-1) = (3\cdot y + 2\cdot (-1))\cdot 3
|
3,331 |
a*b/d = a*b/d
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28,963 |
E(X^4) = 0 \Rightarrow 0 = E(X^2)
|
-20,913 |
\frac{9}{9}\cdot \frac{(-4)\cdot y}{y\cdot 2 + 8\cdot (-1)} = \dfrac{1}{y\cdot 18 + 72\cdot \left(-1\right)}\cdot (y\cdot \left(-36\right))
|
9,128 |
-(-b + a)^2 + (a + b)^2 = 4\cdot a\cdot b
|
8,409 |
(3939 - 6 \cdot 606) \cdot x = 303 \cdot x
|
-9,285 |
40 - d*8 = -2*2*2*d + 2*2*2*5
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10,353 |
2\cdot x^2 \geq x^2 + 1\Longrightarrow \dfrac{1}{x^2 + 1} \geq \frac{1}{x^2\cdot 2}
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21,161 |
\left(7 - \phi\right)^3 + (\phi + 1)^3 + (11 + \phi)^3 + \left(-\phi + 7\right) * \left(-\phi + 7\right) * \left(-\phi + 7\right) = 78*\phi^2 + 72*\phi + 2018
|
2,776 |
\cos(\alpha) \cos(x) + \sin(x) \sin(\alpha) = \cos(\alpha - x)
|
-10,412 |
-\frac{5 \cdot m + 30}{m \cdot 20} = \tfrac{5}{5} \cdot (-\dfrac{6 + m}{m \cdot 4})
|
20,255 |
1 > 1 - \frac{1}{8} = 7/8 = \frac{1}{32}\times 28 \gt 1/2 + \frac{1}{32} = 17/32 \gt \cdots
|
-20,017 |
\dfrac77\cdot \left(h + 6\cdot (-1)\right)/(-2) = \frac{1}{-14}\cdot (42\cdot (-1) + 7\cdot h)
|
-10,562 |
\frac{4}{5p + 5(-1)} \frac{4}{4} = \dfrac{16}{20 p + 20 (-1)}
|
22,180 |
(240 - 6 \cdot y)/12 + y = y/2 + 20
|
36,032 |
\cos^3{x}\cdot 4 - \cos{x}\cdot 3 = \cos{x\cdot 3}
|
14,254 |
2\left(-1\right) + \sqrt{x + 2} = y \Rightarrow 2(-1) + (2 + y)^2 = x
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-5,630 |
\frac{1}{10 (c + 6) \left(c + 8 (-1)\right)} ((c + 6)*10 - (c + 8 \left(-1\right))*10 + 30) = \dfrac{(c + 6)*10}{10 (c + 6) (c + 8 (-1))} - \frac{1}{10 (6 + c) (c + 8 \left(-1\right))} (-80 + c*10) + \frac{30}{(c + 8 (-1)) (c + 6)*10}
|
25,610 |
\sin(2x) = 2\sin(x) \cos(x) = 2\sin\left(x\right) \sqrt{1 - \sin^2(x)}
|
2,665 |
\dfrac{6!}{1! \cdot 2! \cdot 3!} = 60
|
39,948 |
3^{1/k} = 3^{1/k}
|
15,427 |
(x - d) \cdot (d + x) = x^2 - d^2
|
-5,966 |
\frac{1}{\left(l + 9 \cdot (-1)\right) \cdot 3} \cdot 4 = \frac{1}{27 \cdot (-1) + 3 \cdot l} \cdot 4
|
35,916 |
2 \cdot 2^2 \cdot 7^3 = 2744
|
2,636 |
4 = \left(a*b + b + c + c*a\right)/3 \geq ((a*b*c)^2)^{\tfrac{1}{3}}
|
48,496 |
\dfrac{1}{3\cdot 2/3} = \frac{1/3\cdot \frac{3}{2}}{2/3\cdot 3/2} = \frac{\frac13\cdot \frac32}{2/3\cdot \tfrac{1}{2}\cdot 3} = 3\cdot 1/2/3
|
30,624 |
\frac{6!}{2!\cdot (6 + 2\cdot (-1))!} + \frac{1}{(4 + 3\cdot \left(-1\right))!\cdot 3!}\cdot 4! = 19
|
-24,179 |
\left(6 + 4\right)^2 = 10^2 = 10 * 10 = 100
|
31,685 |
\frac{3^{119}}{4} = \frac{599003433304810403471059943169868346577158542512617035467}{4} \cdot 1
|
17,547 |
2655/425 = 2655*1/5/(425*\tfrac15) = \frac{531}{85}
|
39,913 |
\dfrac{\sqrt{2}\times 2}{\sqrt{2} + 2} = 2\times \sqrt{2} - 2
|
4,601 |
e^{-x^2}*(-2*x) = (x * x*4 - 2)*e^{-x^2}
|
-28,986 |
4\times \pi/4 = \pi
|
1,517 |
y\times (\alpha\times G + B\times \beta) = \beta\times B\times y + \alpha\times G\times y
|
-7,465 |
9/2 = \frac{1}{6}\cdot 27
|
-11,964 |
4/15 = \frac{p}{20\cdot \pi}\cdot 20\cdot \pi = p
|
-13,266 |
3 \times (8 + 5) = 3 \times 13 = 39
|
1,194 |
\left(h_2 - h_1\right) \cdot (h_2^{(-1) + l} + h_1 \cdot h_2^{l + 2 \cdot (-1)} + \dots + h_2 \cdot h_1^{l + 2 \cdot (-1)} + h_1^{(-1) + l}) = h_2^l - h_1^l
|
2,892 |
(-1/b + b)^2 > 0\Longrightarrow 2 < b^2 + \frac{1}{b^2}
|
22,417 |
t^3 = t \times t \times t
|
-11,826 |
\frac{9.411}{100} = 9.411\cdot 0.01
|
33,361 |
g^2 - d^2 = \left(g - d\right)*(d + g)
|
14,225 |
a\cdot b\cdot c = a^2\cdot b^2\cdot c = (a^2\cdot b \cdot b) \cdot (a^2\cdot b \cdot b)\cdot c \cdot c = a^4\cdot b^4\cdot c^2
|
12,352 |
-4\cdot \sin{-(\pi/2 - t\cdot 2)} = -4\cdot \sin(-\frac{\pi}{2} + 2\cdot t)
|
-26,661 |
\left(p*2 + 5*s\right)*\left(2*p - s*5\right) = \left(2*p\right)^2 - \left(s*5\right)^2
|
31,052 |
(1 - y^2 + y^4) \cdot (1 + y^2) = 1 + y^6
|
-19,743 |
\dfrac{30}{9} \cdot 1 = \dfrac{30}{9}
|
-5,687 |
\tfrac{3}{(n + \left(-1\right))\cdot 2} = \tfrac{1}{2\cdot n + 2\cdot \left(-1\right)}\cdot 3
|
2,942 |
\left(3 \cdot (-1) + y^2\right) \cdot \left(y \cdot y + \left(-1\right)\right) = y^4 - 4 \cdot y^2 + 3
|
24,928 |
e^Y*e^U = e^{Y + U}
|
16,639 |
R_m - R_{m + 2(-1)} = 7 = R_{m + 2(-1)} - R_{m + 4\left(-1\right)} \implies R_m - R_{2(-1) + m} \cdot 2 + R_{m + 4(-1)} = 0
|
-5,439 |
0.59\cdot 10^{\left(-3\right)\cdot (-1) - 2} = 10^1\cdot 0.59
|
-10,885 |
\frac{160}{4} = 40
|
15,040 |
\frac1q \cdot (1 - q) \cdot \frac{q \cdot q}{-q^2 + 1} = \dfrac{q}{1 + q}
|
34,787 |
\binom{k + \left(-1\right)}{-p + k} = \binom{(-1) + k}{p + (-1)}
|
36,987 |
17^2 + 4\cdot (-1) = 285
|
37,180 |
\varepsilon \cdot \varepsilon + \varepsilon \cdot z \cdot 2 + (-1) = 0\Longrightarrow -z \pm \left(1 + z^2\right)^{1/2} = \varepsilon
|
9,882 |
\cos{π/3} + \cos{2/3\cdot π} = 0
|
-426 |
(e^{\dfrac{3}{4} \times \pi \times i})^{11} = e^{11 \times \frac34 \times i \times \pi}
|
39,806 |
\binom{10}{3} = \frac{10!}{3!\cdot 7!}
|
502 |
1 = C \cdot 4 \Rightarrow C = 1/4
|
6,207 |
5^{2\cdot n} + (-1) = 25^n + (-1) = (25 + (-1))\cdot (1 + 25 + 25 \cdot 25 + \cdots + 25^{n + \left(-1\right)})
|
-12,027 |
\frac{3}{10} = \dfrac{r}{16\cdot π}\cdot 16\cdot π = r
|
11,996 |
\frac13 + 1/12 = 5/12
|
11,597 |
10^{k + 2} + 10^k + 10^{1 + k} = 10^k\cdot (100 + 1 + 10)
|
-4,414 |
\dfrac{x + 45 \cdot (-1)}{25 \cdot (-1) + x^2} = -\frac{1}{5 \cdot (-1) + x} \cdot 4 + \frac{5}{x + 5}
|
2,154 |
10 = \frac{g^2}{4\cdot x^2}\cdot x - g/(2\cdot x)\cdot g + f = -\tfrac{g^2}{4\cdot x} + f
|
-5,067 |
10^3*0.3 = 10^{(-2) (-1) + 1}*0.3
|
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