id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
5,970 |
98*100 + 2 = \left(99 + (-1)\right)*(99 + 1) + 2 = 99^2 + (-1) + 2 = 99^2 + 1
|
9,426 |
3^5 - ((-1) + 3)^5\cdot {3 \choose 1} + (3 + 2\cdot (-1))^5\cdot {3 \choose 2} = 150
|
16,547 |
(m + 1/2)^2 = 1/4 + m^2 + m
|
20,898 |
\sigma * \sigma = (\sqrt{n + \sqrt{n + \sqrt{n + ...}}})^2 = n + \sigma
|
51,976 |
\frac{n}{n^2 + n} + \dotsm + \frac{n}{n^2 + 1} \lt x_n < \dfrac{n}{n^2 + 1} + \dotsm + \frac{n}{n^2 + 1}\Longrightarrow \frac{1}{n^2 + n}\cdot n^2 < x_n \lt \dfrac{1}{n^2 + 1}\cdot n^2
|
-4,553 |
\frac{4}{4 \times \left(-1\right) + x} + \dfrac{3}{2 \times (-1) + x} = \frac{20 \times (-1) + x \times 7}{8 + x^2 - x \times 6}
|
16,422 |
(-1) + x \cdot x = \left(x + 1\right) \left((-1) + x\right)
|
6,859 |
(2 \cdot (-1) + 1)^2 + (0 + (-1))^2 + (2 \cdot (-1) + 0)^2 = 6
|
36,615 |
0 - y = -y \in X
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6,452 |
0 = 3\cdot (-1) + z^3 - z\cdot 3 \Rightarrow z = 2.1038
|
-7,571 |
\frac{-18 \cdot i + 6}{4 - 2 \cdot i} = \frac{1}{4 - i \cdot 2} \cdot (6 - 18 \cdot i) \cdot \dfrac{2 \cdot i + 4}{4 + i \cdot 2}
|
22,822 |
\operatorname{E}\left[T^2\right] = \operatorname{E}\left[T\right]^2
|
10,287 |
1 = \frac{1}{a} \cdot a \Rightarrow \dfrac{1}{\frac{1}{a}} = a
|
24,171 |
(1 + 2)\cdot p = 3\cdot p
|
32,511 |
(k + 1)! - k! = k \cdot k!
|
-3,140 |
-2^{\frac{1}{2}} + 18^{1 / 2} + 50^{\frac{1}{2}} = -2^{1 / 2} + (9 \cdot 2)^{1 / 2} + \left(25 \cdot 2\right)^{\frac{1}{2}}
|
44,389 |
4\times 7\times 13 = 364
|
-5,472 |
\dfrac{1}{(10 + q) \cdot (q + 2) \cdot 9} \cdot (q \cdot 6 + 12) - \frac{15 \cdot \left(10 + q\right)}{9 \cdot (q + 2) \cdot (q + 10)} + \frac{q \cdot 36}{(10 + q) \cdot \left(2 + q\right) \cdot 9} = \frac{36 \cdot q + 6 \cdot (q + 2) - (10 + q) \cdot 15}{9 \cdot (q + 2) \cdot (10 + q)}
|
28,390 |
(j + 2)! = (2 + j)\cdot (1 + j)\cdot j\cdot ...
|
-18,439 |
\dfrac{(3\times (-1) + q)\times (10\times (-1) + q)}{q\times (q + 10\times (-1))} = \dfrac{1}{q^2 - 10\times q}\times (q^2 - 13\times q + 30)
|
8,809 |
\frac{1}{y + 1}\cdot \left(3\cdot y + 2\cdot (-1)\right) = \dfrac{1}{y + 1}\cdot \left(3\cdot (y + 1) + 5\cdot (-1)\right) = 3 - \frac{5}{y + 1}
|
11,780 |
H^{1 + n} = H^n\cdot H
|
7,119 |
d/dx (\left(x + (-1)\right) \left(x + 1\right)^3) = ((-1) + x) (x + 1) \cdot (x + 1)\cdot 3 + (x + 1)^3
|
24,668 |
0.352 = \frac{8^2}{20^2} + 2\frac{8^2}{20^2}*\frac{1}{20}12
|
252 |
\dfrac{1}{h_1 \cdot h_2} + \tfrac{1}{(h_2 + (-1)) \cdot h_2 \cdot h_1} = \frac{1}{h_1 \cdot \left((-1) + h_2\right)}
|
22,812 |
c_1 - 1/2 + 10/4 = 0 \Rightarrow c_1 = -2
|
19,068 |
-\frac{25}{7} = \sec{x} \Rightarrow -7/25 = \cos{x}
|
30,563 |
3 \cdot 3 + 1^2 - 3 = 7
|
-4,704 |
\dfrac{y*3 + 14}{y^2 + 4(-1)} = -\frac{2}{y + 2} + \frac{5}{y + 2\left(-1\right)}
|
22,001 |
x - \tfrac{1}{3!}\cdot x^3 + \dfrac{x^5}{5!} - ... = \sin{x}
|
428 |
(2 \cdot 10^{1/2})^2 + \left(5 \cdot 10^{1/2}\right)^2 = 40 + 250 = 290 = (290^{1/2})^2
|
20,002 |
y^3 - \left(5 + i\right) y \cdot y + y \cdot (i \cdot 5 + 2) + 10 (-1) = (5(-1) + y) (y \cdot y - iy + 2)
|
5,956 |
(z - y) \cdot (z^1 + z^0 \cdot y + \ldots + z \cdot y^0 + y^1) = z^2 - y^2
|
19,013 |
\tan^{-1}(∞) = \frac{1}{2} \cdot \pi
|
-5,412 |
2.56 \cdot 10 = \frac{2.56}{10^6} \cdot 10 = \dfrac{2.56}{10^5}
|
37,037 |
\sin(f + g) = \sin\left(f\right) \cdot \cos(g) + \sin(g) \cdot \cos\left(f\right)
|
10,398 |
g^{h + b} = g^b \cdot g^h
|
11,879 |
\sqrt{l + 3} = (l + 2)^2 + (-1) = (l + 3)^2 - 2 \cdot (l + 3)
|
-25,026 |
-1 - y - y \cdot y - y^3 - y^4 - \ldots = -\frac{1}{-y + 1}
|
-19,304 |
3/4*3/7 = \frac{3*\frac14}{7*\frac{1}{3}}
|
7,070 |
-3\cdot d_2\cdot g\cdot d_1 + d_2^3 + g^3 + d_1 \cdot d_1 \cdot d_1 = \tfrac{1}{2}\cdot (d_1 + d_2 + g)\cdot \left((-g + d_1)^2 + (d_2 - g)^2 + (-d_1 + d_2)^2\right)
|
37,973 |
F + Q := F \cup Q
|
26,344 |
l + n + 1 + 1 = 1 + n + 1 + l
|
9,452 |
(a + l) \cdot (a + l) = a^2 + 2\cdot a\cdot l + l^2 = i + 2\cdot a\cdot l - i = 2\cdot a\cdot l
|
52,557 |
349 = 205 + 144
|
26,501 |
p \times {k \choose p} = {k + (-1) \choose (-1) + p} \times k
|
15,901 |
2*\left(2 + 3*n\right) = 4 + 6*n
|
26,652 |
s^6 s^{12} = s^{18}
|
11,595 |
\sqrt{2} + 5^{1/3} = y rightarrow \left(-\sqrt{2} + y\right)^3 = 5
|
9,131 |
\left(o^y + 3\right) (o^y + (-1)) + 4 = o^{2y} + 2o^y + 1 = (o^y + 1)^2
|
27,625 |
x = \pi/4 \implies \cos^5(x) - \sin^5(x) = 0 \neq \cos(5 \cdot \pi/4)
|
-6,693 |
\frac{8}{10} + \frac{1}{100}\cdot 3 = \tfrac{3}{100} + \frac{1}{100}\cdot 80
|
-19,691 |
\frac{15}{7} = \frac{5\cdot 3}{7}
|
37,373 |
a = h \Rightarrow a = h
|
6,192 |
\frac{1}{1 + m}m = 1 - \tfrac{1}{1 + m}
|
4,064 |
\mathbb{E}(R - Y)^2 + Var(-Y + R) = \mathbb{E}((R - Y)^2)
|
8,818 |
\frac{657720}{30^4}*1 = \frac{203}{250}
|
24,758 |
\sin\left(y + z\right) = \sin(y) \cos(z) + \cos(y) \sin(z)
|
40,906 |
\frac{4!}{\left(4 + 2 \cdot (-1)\right)! \cdot 2!} = \dfrac{1}{2 \cdot 2} \cdot 24 = 6
|
-20,393 |
\frac{-14 \cdot t + 56 \cdot (-1)}{t \cdot 70 + 35} = 7/7 \cdot \tfrac{8 \cdot (-1) - 2 \cdot t}{5 + t \cdot 10}
|
7,221 |
(z + x) \cdot \left(x^2 - x \cdot z + z^2\right) = z \cdot z \cdot z + x^3
|
16,123 |
2\cdot 1/31/25 = \frac{1}{775}\cdot 2
|
15,851 |
-\frac{1}{6}\cdot 2\cdot \frac15\cdot 2 + 1 = \frac{13}{15}
|
20,658 |
(1 - \cos\left(4\cdot x\right))^{\frac{1}{2}} = \left(2\cdot \sin^{22}(x)\right)^{1 / 2} = 2^{1 / 2}\cdot |\sin(2\cdot x)|
|
14,626 |
16 + 9^k - 1^k = 15 + 3^{k*2}
|
-21,028 |
-7/5 \cdot \frac{4 + z}{z + 4} = \tfrac{28 \cdot (-1) - 7 \cdot z}{z \cdot 5 + 20}
|
28,572 |
\sin(z + 2 \cdot \pi) = \Im{\left(e^{i \cdot z + i \cdot 2 \cdot \pi}\right)} = \Im{(e^{i \cdot z})} = \sin\left(z\right)
|
8,374 |
2 - 2\cdot a\Longrightarrow 2\cdot (1 - a) = 0
|
-22,030 |
\frac{1}{7}*10 = \dfrac{40}{28}
|
1,642 |
\dfrac12\cdot (3\cdot (-1) + \sqrt{3 + \sqrt{2}\cdot 2} \cdot \sqrt{3 + \sqrt{2}\cdot 2}) = \sqrt{2}
|
16,410 |
4^n + 15 \cdot n + \left(-1\right) = (3 + 1)^n + 15 \cdot n + \left(-1\right)
|
17,896 |
0 = x^3 - x + 24 (-1)\Longrightarrow 3 = x
|
21,185 |
-\frac{3*x + 4*y}{5*z - 8*w} = -\dfrac{(3*x - 4*y)*(-1)}{\left(5*z - 8*w\right)*(-1)} = \frac{3*x + 4*y}{8*w - 5*z}
|
-12,038 |
\frac13\cdot 2 = s/(16\cdot \pi)\cdot 16\cdot \pi = s
|
-22,123 |
\frac18 \cdot 40 = 5
|
-3,858 |
\dfrac{63}{54}\cdot \frac{1}{x^5}\cdot x^5 = \frac{63\cdot x^5}{x^5\cdot 54}
|
32,371 |
g \cdot f + d \cdot g + f \cdot d = \left(-(g^2 + f \cdot f + d^2) + (g + f + d)^2\right)/2
|
3,260 |
(a^2 + a*f + f^2)*(a - f) = a * a * a - f^3
|
-2,885 |
\sqrt{3}*2 = \sqrt{3}*(5 + 1 + 4 (-1))
|
13,457 |
\sqrt{2\cdot y + 1} = y - (y^2 - 2\cdot y + 1)/7 = \dfrac17\cdot (-y^2 + 9\cdot y + 1)
|
24,080 |
\|x_t - x_{1 + t}\|^2 \leq 0 \Rightarrow x_t = x_{t + 1}
|
2,108 |
\frac{1}{a \cdot \frac{1}{b}} = \dfrac{b}{a}
|
-16,844 |
8 = 8*5*p + 8*(-1) = 40*p - 8 = 40*p + 8*(-1)
|
-12,252 |
\frac{1}{18}*17 = \frac{s}{18*\pi}*18*\pi = s
|
25,299 |
q^2 + 2*w*q + w^2 = \left(q + w\right) * \left(q + w\right)
|
22,300 |
\frac{5!}{(5 + 2\cdot \left(-1\right))!}\cdot \frac{10!}{(10 + 3\cdot (-1))!}\cdot 7!\cdot \frac{1}{(7 + 2\cdot (-1))!}\cdot 3! = 720\cdot 42\cdot 20\cdot 6 = 3628800
|
-20,087 |
\frac{5 (-1) + y}{3 y + 4}*\tfrac{7}{7} = \frac{1}{28 + 21 y} (7 y + 35 (-1))
|
31,023 |
49 \cdot \left(-1\right) + 3 \cdot 11 \cdot 11 = 314
|
15,221 |
B\cdot \mathbb{E}\left(x\right) = B\cdot \mathbb{E}\left(x\right)
|
9,466 |
\sin{b} \sin{x} + \cos{b} \cos{x} = \cos(-b + x)
|
6,209 |
\ln\left(2\right)/\left(\ln(4)\right) = \frac{1}{2}
|
22,182 |
A\cdot x - x\cdot A = A \Rightarrow A^2 = A^2\cdot x - A\cdot A\cdot x
|
-21,015 |
-7/5*\frac{10*k}{10*k} = \frac{(-70)*k}{50*k}
|
-23,635 |
3/28 = \frac{3\cdot 1/4}{7}
|
45,482 |
-\frac82 = -\frac82
|
4,710 |
\frac{1}{16^{\frac14 \cdot 3} \cdot 27^{2/3}} = \frac{1}{\left(27^2\right)^{1/3} \cdot (16^3)^{\frac{1}{4}}}
|
6,829 |
g*(b*a + b*a) = (b*a + b*a)*g
|
7,242 |
-\frac14\pi = \frac14((-1) \pi)
|
19,825 |
\left(k + 2\right)\cdot (k + 3) - 5\cdot (2 + k) + 4 = k^2
|
8,303 |
x^2 + x \cdot 2 + 1 = \left(x + 1\right)^2
|
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