id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
20,137 |
2\cdot m^{1/2}/2 - \frac{m^{1/2}}{2} = \dfrac{1}{2}\cdot m^{1/2}
|
21,162 |
2 - 2f > 0 \implies f \lt 1
|
-25,800 |
\frac{2}{5*3} = \frac{1}{15}*2
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22,400 |
\frac{1}{4\tau}(x^2 \tau^2*4 + 4\tau bx + 4f\tau) = x^2 \tau + bx + f
|
-20,127 |
\tfrac{1}{m \times 81} \times (54 \times (-1) - 54 \times m) = \frac{1}{m \times 9} \times (-6 \times m + 6 \times (-1)) \times 9/9
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18,748 |
f^b = ff^{b + (-1)} = f\cdot (f \cdot f)^{\dfrac12(b + (-1))}
|
2,230 |
0 = (g + b - c)*x^2 + 2*(g + b)*x + g + b + c = (g + b)*(x + 1)^2 - c*(x^2 + \left(-1\right))
|
25,709 |
X \geq 0 \implies 0 \leq E(X)
|
5,515 |
\frac{1}{2\times k} = \frac{1}{k\times 2} = 1/\left(2\times k\right)
|
28,483 |
2 \cdot (-1) + \cos^2{x/2} \cdot 4 = 2 \cdot \cos{x}
|
-19,233 |
5/12 = Y_q/(81 \pi)*81 \pi = Y_q
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52,684 |
(-1) + 100 = 99
|
21,343 |
\sin(R \cdot 2) = \cos(R) \sin(R) \cdot 2
|
27,039 |
\left(x + g h\right)/g = 0 g + \frac{x}{g} + h
|
-19,121 |
59/60 = A_s/\left(16 \pi\right)*16 \pi = A_s
|
-12,490 |
\frac13\cdot 135 = 45
|
-24,755 |
\cos\left(\frac{\pi\cdot 7}{12}\right) = \left(-\sqrt{6} + \sqrt{2}\right)/4
|
4,305 |
a^2 \cdot a = a^2 \cdot a \neq a \cdot a^2
|
1,771 |
f \cdot f^{k \cdot 2} = f^{1 + 2 \cdot k}
|
27,423 |
u_w = u_v x \Rightarrow u_v = u_w/x
|
27,293 |
n^2 + 1 * 1 = n^2 + 1
|
9,381 |
z^2*6 + \left(1 + 5S\right) z + S^2 + S*2 + 15 (-1) = 15 (-1) + 6z * z + 5zS + S^2 + z + 2S
|
29,867 |
8 = 2 + 2 + 2*2
|
31,352 |
\cos^2(c) a = b - \cos(c) rightarrow a\cos^2(c) + \cos(c) - b = 0
|
8,945 |
3/2 \cdot (1 + 1/3) = 2
|
-17,206 |
\frac{\sec^2\left(\theta\right)}{\sec^2\left(\theta\right)} = \dfrac{1}{\sec^2(\theta)}(\tan^2\left(\theta\right) + 1)
|
-3,321 |
\sqrt{208} - \sqrt{117} = -\sqrt{9 \cdot 13} + \sqrt{16 \cdot 13}
|
25,457 |
\left(1 + 2 \cdot \sqrt{t} + t = t + 9 \Rightarrow 4 = \sqrt{t}\right) \Rightarrow 16 = t
|
1,167 |
(-p + n)/n \cdot \tfrac{p}{n + (-1)} = \frac{1}{-n + n^2} \cdot \left(n \cdot p - p^2\right)
|
-27,735 |
\frac{\mathrm{d}}{\mathrm{d}f} \left(-2 \cdot \cot(f)\right) = -2 \cdot \frac{\mathrm{d}}{\mathrm{d}f} \cot(f) = 2 \cdot \csc^2\left(f\right)
|
7,412 |
y * y + 4*y^4 + 4*y^3 = y^4*4 + 2*y^3 + y * y * y*2 + y^2
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-20,630 |
8/8 \frac{-6n + 2}{n \cdot (-5)} = \frac{1}{(-40) n}(16 - 48 n)
|
12,456 |
(z - 2\cdot y)\cdot (z - y) = z^2 + 2\cdot y^2 - y\cdot z\cdot 3
|
-21,099 |
\dfrac{3}{10} = \dfrac{30}{100}
|
-19,586 |
\frac45\cdot 7/6 = \frac{\frac{1}{5}\cdot 4}{1/7\cdot 6}
|
11,974 |
(b + g)^2 = b^2 + g^2 + 2\cdot b\cdot g
|
28,024 |
-7 * 7 * 7 = (45 + 29*\sqrt{2})*(\sqrt{2}*29 + 45*(-1))
|
-10,702 |
\frac{1}{12}\cdot 12\cdot \left(-\frac{3}{4\cdot a + 4}\right) = -\frac{36}{a\cdot 48 + 48}
|
21,591 |
(E(X)*E(V))^2 = E(X*V)^2
|
13,738 |
(\dfrac{1}{3})^3 + (\frac23)^3 = 1/3
|
33,791 |
\frac{1}{y + 1} = \dfrac{1}{y\times (1 + \dfrac{1}{y})}
|
702 |
(5^3)^k = 5^{3*k}
|
-21,733 |
-\dfrac18\cdot 41 = -41/8
|
7,900 |
-c + x \geq 0 \Rightarrow x \geq c
|
4,144 |
-e\cdot (-b) = --e\cdot b = e\cdot b = e\cdot b
|
13,696 |
x^2 + 4 \cdot x + 5 \cdot \left(-1\right) = \left(x + 2 + 3\right) \cdot (x + 2 + 3 \cdot (-1)) = (x + 5) \cdot \left(x + \left(-1\right)\right)
|
1,186 |
(2 \cdot \frac{1}{3})^2 + (2 \cdot 2/3)^2 = 20/9 \gt 2
|
35,378 |
f/h = \frac{1}{h\frac1f}
|
9,637 |
g \cdot h \cdot f = (g^2 + h^2) \cdot f = (g^2 + h \cdot h) \cdot (g^2 + h \cdot h) + f^2
|
9,286 |
\dfrac{1}{2}*(-1 + \sqrt{17}) = \sqrt{17}/2 - 1/2
|
-3,469 |
25/100 = \tfrac{5 \cdot 5}{5 \cdot 20}
|
-1,742 |
-\pi\cdot \dfrac{5}{4} + \frac23\cdot \pi = -\pi\cdot \frac{1}{12}\cdot 7
|
24,791 |
15*(15*(-1) + 2*h) + 225 = h*30
|
578 |
\frac{1}{d h} = 1/(h d)
|
31,308 |
Y^{o + n} = Y^o Y^n
|
41,022 |
7586 = 6^2 \cdot 6 + 9^3 + 12^3 + 17^3
|
30,260 |
z\cdot x + x'\cdot y = z\cdot x + x'\cdot y + y\cdot z
|
16,352 |
15/x = \frac23 \implies 22.5 = x
|
-15,980 |
-\frac{9}{10}*9 + \frac{6}{10} = -75/10
|
50,704 |
\tbinom{9}{5} = 126
|
1,354 |
-1/2 = \sin(((-1) \cdot \pi)/6)
|
30,183 |
(1 + x^2)\cdot \operatorname{atan}(x) - \operatorname{atan}(x) = \operatorname{atan}\left(x\right)\cdot x \cdot x
|
2,011 |
\dfrac{1}{2*z_1^2 + z_1*z_2 - z_2^2}*(-z_2 * z_2 + 2*z_1 * z_1 - z_1*z_2) = 1 - \dfrac{z_2*z_1*2}{-z_2^2 + z_1 * z_1*2 + z_1*z_2}
|
-18,968 |
9/10 = \frac{A_s}{100\cdot \pi}\cdot 100\cdot \pi = A_s
|
-20,854 |
\dfrac{1}{q + 10 \cdot (-1)} \cdot (q \cdot 4 + 40 \cdot (-1)) = 4/1 \cdot \frac{q + 10 \cdot (-1)}{10 \cdot (-1) + q}
|
11,377 |
\frac{21}{8} = \dfrac{1}{8}9 + \dfrac{1}{2} + \dfrac144
|
26,870 |
-80 \cdot 80 + 7500 - 60 \cdot 20 = -100
|
6,366 |
(n - k + 1 + 1)! = (n - k)!
|
34,440 |
\frac{1}{7!}*{7 \choose 5} = 1/240
|
20,000 |
n^{a + b} = n^a*n^b
|
-18,800 |
y = \frac{2*y}{2}*1
|
-20,381 |
-\frac75\cdot \dfrac{5\cdot (-1) - n}{5\cdot (-1) - n} = \frac{7\cdot n + 35}{-5\cdot n + 25\cdot \left(-1\right)}
|
1,101 |
\frac{1}{\sin{x}} = \tfrac{\sin{x}}{\sin^2{x}}
|
33,291 |
\dfrac{l}{l + 1} \cdot 2 = \dfrac{\dfrac{1}{1 + l}}{\frac{1}{l} \cdot 2^l} \cdot 2^{1 + l}
|
20,902 |
v_1 + i\cdot b_1 + v_2 + b_2\cdot i = i\cdot (b_1 + b_2) + v_1 + v_2
|
-19,167 |
\frac{11}{30} = \frac{A_s}{9 \times \pi} \times 9 \times \pi = A_s
|
30,466 |
100 - 50 - 33 + 16 = 33
|
29,228 |
\operatorname{P}\left(l\right) \coloneqq \tfrac{1}{x^l} \coloneqq (1/x)^l
|
-23,680 |
\frac{2}{5}\cdot \dfrac58 = \frac{1}{4}
|
15,507 |
-1 = \left(-1\right)^2 * (-1) = (-1)^{6/2} = \sqrt{(-1)^6} = 1
|
-11,955 |
\frac{13}{15} = \frac{p}{12*\pi}*12*\pi = p
|
28,989 |
\cos^2(\frac12 \cdot \pi - y) = \sin^2(y) = 1 - \cos^2\left(y\right)
|
-4,832 |
7.92 \cdot 10 = \frac{7.92}{10^7} \cdot 10 = \frac{1}{10^6} \cdot 7.92
|
9,795 |
b = c \implies b = c
|
2,913 |
\frac{7*12}{2} = 42
|
26,528 |
(y + 1) \times (y + (-1)) = (-1) + y^2
|
51,702 |
\frac{\cos{\pi\cdot y\cdot i}}{\sin{\pi\cdot y\cdot i}} - (\pi\cdot y\cdot i)^{-1} = \frac{1}{\pi}\cdot \sum_{x=1}^\infty ((y\cdot i + x)^{-1} + (y\cdot i - x)^{-1}) = 2\cdot y/(\pi\cdot i)\cdot \sum_{x=1}^\infty \tfrac{1}{y^2 + x^2}
|
25,188 |
(a + c)*m = a*m + m*c
|
25,624 |
\frac{1}{4}\cdot ({49 \choose 2} - ((-1) + 49)/2) + \frac{1/2}{2}\cdot (49 + (-1)) = 300
|
-26,463 |
(-3*z + 2) * (-3*z + 2) = 2 * 2 - 2*3*z*2 + \left(3*z\right)^2
|
6,069 |
1 = Z + x \Rightarrow Z = 1 - x
|
11,856 |
\int \frac{(-1) - s\cdot 2 + \left(-1\right)}{s \cdot s\cdot 4 + 4}\cdot 2\,ds = -\int \dfrac{1}{s^2 + 1}\left(1 + s\right)\,ds
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-8,544 |
\frac{1}{5} \cdot 4 - 1/8 = \frac{8}{5 \cdot 8} \cdot 4 - \frac{5}{8 \cdot 5} = \dfrac{1}{40} \cdot 32 - \frac{5}{40} = \dfrac{1}{40} \cdot (32 + 5 \cdot (-1)) = \frac{1}{40} \cdot 27
|
-18,426 |
\frac{x^2 - x \cdot 6}{x^2 - 16 \cdot x + 60} = \frac{x}{\left(10 \cdot \left(-1\right) + x\right) \cdot (6 \cdot (-1) + x)} \cdot (x + 6 \cdot \left(-1\right))
|
9,728 |
0 = v \implies \dfrac{1}{v}
|
19,766 |
\left|{A^V A}\right| = \left|{AA^V}\right|
|
42,866 |
11!*72 = 6*6*10!*11*2
|
-10,526 |
4/4 \frac{1 + q}{q^3 \cdot 4} = \dfrac{1}{q^3 \cdot 16}(q \cdot 4 + 4)
|
-19,309 |
\dfrac71\cdot 9/2 = \dfrac{9 / 2}{\frac{1}{7}}\cdot 1
|
25,108 |
10^{d + b} = 10^d\cdot 10^b
|
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