id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
906 |
-y_4\times 5 - 2\times y_2 - 5\times y_3 = 0 \implies y_2 = -(y_3 + y_4)\times 5/2
|
34,052 |
\sin(z + i y) = \sin(z) \cos\left(i y\right) + \cos(z) \sin(i y) = \sin(z) \cosh\left(y\right) + i \cos(z) \sinh(y)
|
23,245 |
13\cdot 29\cdot 28/(1\cdot 2) = 5278
|
-22,307 |
r^2 + 3\cdot r + 2 = (r + 2)\cdot (r + 1)
|
-7,648 |
\frac{-20 - i \cdot 30}{-i - 5} = \frac{1}{-5 + i} \cdot \left(-5 + i\right) \cdot \dfrac{1}{-i - 5} \cdot \left(-20 - 30 \cdot i\right)
|
-1,247 |
\dfrac{30}{35} = \tfrac{30 \cdot 1/5}{35 \cdot \frac15} = \frac67
|
31,477 |
4\cdot (5 + 3\cdot m \cdot m + 6\cdot m) = (2\cdot m + 4)^2 + (2\cdot m) \cdot (2\cdot m) + (m\cdot 2 + 2)^2
|
-4,268 |
\tfrac{1}{f^3}*f^4 = \frac{f}{f*f*f}*f*f*f = f
|
4,874 |
2^{\frac{1}{3} \cdot (n + 1)} = 2^{1/3} \cdot 2^{\dfrac{1}{3} \cdot n} > n \cdot 2^{\frac13}
|
29,587 |
4 + 6 \times (-1) = 1 + 3 \times (-1)
|
-19,740 |
5*9/(7) = 45/7
|
-2,435 |
\sqrt{7}*(2 + 3*(-1) + 4) = 3*\sqrt{7}
|
-29,380 |
\left(1 + 6x\right) (1 - 6x) = 1^2 - (6x)^2 = 1 - 36 x^2
|
-10,394 |
-\frac{1}{2 + 4*z}*(8 + z)*4/4 = -\frac{z*4 + 32}{8 + 16*z}
|
-579 |
(e^{\pi \cdot i \cdot 5/3})^{16} = e^{16 \cdot \frac53 \cdot i \cdot \pi}
|
-23,428 |
\frac{3}{20} = \frac{3 / 4}{5}\cdot 1
|
16,577 |
\left(y = z * z + 4(-1) \Rightarrow z^2 = y + 4\right) \Rightarrow (y + 4)^{1/2} = (z^2)^{1/2}
|
4,485 |
\dfrac{3\times \frac{1}{10}}{3/10 + 1/10} = \frac14\times 3
|
-2,724 |
\sqrt{9*3} + \sqrt{16*3} = \sqrt{27} + \sqrt{48}
|
4,438 |
\tfrac{1}{7}\cdot (2^6 + (-1)) = (64 + (-1))/7 = 63/7 = 9
|
-22,803 |
\frac{16 \cdot 3}{4 \cdot 16} = \frac{1}{64} \cdot 48
|
7,894 |
a_j = 2 \cdot a_j
|
-6,293 |
\dfrac{1}{45 + 5\cdot n} = \frac{1}{5\cdot (9 + n)}
|
22,671 |
(x^2)^2 \cdot x^2 + 64 = x \cdot x \cdot (x^2)^2 + 4^3 = \left(x \cdot x + 4\right)\cdot \left(x^4 - 4\cdot x^2 + 16\right)
|
-29,562 |
\frac{1}{y} ((-1) + 6 y^5 - 2 y^4) = -1/y + \frac6y y^5 - \frac{y^4}{y} 2
|
6,567 |
\cot(x) - \tan(x) = \frac{1}{\sin\left(x\right)\cdot \cos\left(x\right)}\cdot \left(\cos^2(x) - \sin^2(x)\right) = 2\cdot \cot(2\cdot x)
|
469 |
8*E = 1 \Rightarrow E = \frac18
|
28,181 |
\frac{172}{6} = 52/6 + 20
|
-23,015 |
\frac{4 \cdot 5}{3 \cdot 5} = \dfrac{20}{15}
|
12,938 |
h^2\cdot A_j\cdot x = h^2\cdot x\cdot A_j
|
15,460 |
\int_x^1 \dotsm\,\mathrm{d}x = -\int\limits_1^x \dotsm\,\mathrm{d}x
|
7,870 |
\frac{1}{7^x + \left(-2\right)^x}*(3^x + 5^x) = \tfrac{\left(\frac37\right)^x + (\dfrac57)^x}{(-2/7)^x + 1}
|
5,602 |
e^{h \cdot z} = \frac{1 + h/2 \cdot z}{1 - \frac{h}{2} \cdot z} = \frac{2 + h \cdot z}{2 - h \cdot z}
|
7,501 |
x^{2^m} = (x \times x)^{2^{m + (-1)}} = (x + 1)^{2^{m + (-1)}} = x^{2^{m + (-1)}} + 1
|
-18,812 |
\frac{8}{2}\cdot y = 4\cdot y
|
12,319 |
f^n = f^{(-1) + n}*f
|
-22,435 |
4^{3/2} = (4^{1/2})^3
|
-4,402 |
\frac{q^5}{q^2} = \frac{q}{q q} q q q q = q^3
|
29,241 |
\cosh(\sinh^{-1}{x}) = \sqrt{1 + x^2}
|
-23,722 |
\frac{3}{8}*3/7 = \dfrac{9}{56}
|
3,779 |
-y^2 + y + 2 = (1 + y) \cdot (2 - y)
|
22,978 |
\binom{(-1) + 10 + 3}{3 + \left(-1\right)} = \binom{12}{2}
|
17,105 |
4-4i=2(2-2i)
|
15,030 |
\tfrac{1}{495}\cdot 105 = \frac{7}{33}
|
25,958 |
e\cdot G/e = e\cdot G\cdot e = G
|
-594 |
(e^{\frac{23}{12}i\pi})^{15} = e^{15 \frac{23 i\pi}{12}}
|
-23,042 |
\frac{135}{120} = \frac{15\cdot 9}{8\cdot 15}
|
-28,796 |
1 = \frac{\pi \cdot 2}{2 \cdot \pi}
|
22,308 |
4 \cdot 4\cdot ((-1) + 4^2)/3 = 4 \cdot 4 + 4^3
|
12,047 |
2^2 \cdot (2 + 1) \cdot (2 + 1)/4 = 36/4 = 9
|
-5,548 |
\dfrac{2}{2}\cdot \frac{4}{(5(-1) + k) (k + 7)} = \dfrac{1}{(k + 7) \left(5(-1) + k\right)\cdot 2}8
|
9,135 |
y^2 + 2\cdot y + 4 = y^2 + 2\cdot y + 1 + 3 = (y + 1)^2 + 3
|
10,954 |
-t^2 + t^4 = (t \times t + 2 \times (-1)) \times (t^2 + 1) + 2
|
3,014 |
1 - \dfrac{1}{4\times x^2} = \left(\dfrac{1}{x\times 2} + 1\right)\times (1 - \dfrac{1}{x\times 2})
|
-12,311 |
10^{\frac{1}{2}}*2 = 40^{\frac{1}{2}}
|
12,776 |
\frac{\partial}{\partial x} e^{k*x} = k*e^{x*k}
|
26,275 |
YY^Q = Y^Q Y
|
25,488 |
a_n^2 + (-1) = (a_n + (-1))\cdot \left(1 + a_n\right)
|
-617 |
e^{18 \cdot \frac{\pi}{12} \cdot i} = (e^{i \cdot \pi/12})^{18}
|
18,746 |
\frac{1}{6} + \dfrac16 + 1/6 = \dfrac{1}{2}
|
-4,498 |
\frac{1}{x^2 - x\cdot 4 + 3}\cdot (-x\cdot 6 + 14) = -\frac{4}{(-1) + x} - \tfrac{1}{3\cdot (-1) + x}\cdot 2
|
22,446 |
\left(f\cdot \xi\right)^2 = f \cdot f\cdot \xi \cdot \xi
|
-25,784 |
\frac14 \cdot \frac{11}{12} = \frac{11}{48}
|
33,923 |
(-w + z)\cdot \left(w + z\right) = z^2 - w^2
|
21,066 |
G + e + (-1) = (-1) + e + G
|
-4,452 |
\frac{2}{y + 3} + \frac{1}{y + 2 \cdot (-1)} \cdot 4 = \dfrac{8 + 6 \cdot y}{y^2 + y + 6 \cdot (-1)}
|
29,647 |
0 = b\cdot y\cdot 4 + a\cdot y^4\cdot 4 \Rightarrow y^4\cdot a = -b\cdot y
|
40,594 |
1/105 = \frac{384}{40320}
|
-10,392 |
20/20\times (-\frac{9}{x + 5}) = -\frac{180}{100 + 20\times x}
|
-10,655 |
\frac{1}{12 \cdot t} \cdot (30 + t \cdot 6) = \frac{t + 5}{t \cdot 2} \cdot \tfrac16 \cdot 6
|
12,134 |
1/2 = 2/3 \cdot \tfrac{3}{4}
|
-21,033 |
\dfrac{1}{28\times (-1) - a\times 35}\times \left(12\times (-1) - 15\times a\right) = \frac{4\times (-1) - 5\times a}{-5\times a + 4\times (-1)}\times 3/7
|
-24,754 |
\sin{7 \cdot \pi/12} = \dfrac14 \cdot (\sqrt{2} + \sqrt{6})
|
7,702 |
(3 + z - y) \cdot (z - y + 3 \cdot \left(-1\right)) = (z - 3 + y) \cdot (-(3 \cdot (-1) + y) + z)
|
7,327 |
0 = 1 \cdot (2 \cdot (-1) + 3) - 1 \cdot (2 \cdot (-1) + 3) + (2 \cdot 3 - 2 \cdot 3)
|
2,576 |
\frac{c + 2}{1 - c \cdot 2} = -1 \implies c = 3
|
323 |
\left(i \cdot 16\right)^{-1} = -\frac{1}{16 \cdot i} \cdot 3 + (4 \cdot i)^{-1}
|
-6,592 |
\dfrac{4}{20 + x^2 - x \cdot 12} = \frac{1}{\left(2 \cdot (-1) + x\right) \cdot \left(10 \cdot \left(-1\right) + x\right)} \cdot 4
|
-17,037 |
2 = 2(-3s) + 2\left(-1\right) = -6s - 2 = -6s + 2(-1)
|
12,770 |
14^2 + 2^2 = 15 \cdot 15 - 5^2
|
-2,411 |
\sqrt{6} + 3 \cdot \sqrt{6} = \sqrt{6} + \sqrt{9} \cdot \sqrt{6}
|
11,886 |
-\left(16*(-1) + l\right)*(l + 16)*27 = -l^2*27 + 6912
|
24,842 |
18^2*4 = 4^2 + 16^2 + 32^2
|
-587 |
e^{\tfrac{23}{12} \cdot i \cdot π \cdot 16} = (e^{23 \cdot π \cdot i/12})^{16}
|
8,276 |
4(s - \sqrt{2}) + (x - \sqrt{2}) \cdot (x - \sqrt{2}) \left(x + \sqrt{2} \cdot 2\right) = x^3 - 6x + s \cdot 4
|
-2,682 |
10*\sqrt{6} = \left(5 + 1 + 4\right)*\sqrt{6}
|
4,736 |
-2^2*120*119/2 + 13^4 = 1
|
-3,265 |
\sqrt{2} \cdot \sqrt{25} - \sqrt{2} \cdot \sqrt{9} = 5 \cdot \sqrt{2} - 3 \cdot \sqrt{2}
|
-3,425 |
\sqrt{175} + \sqrt{63} - \sqrt{7} = -\sqrt{7} + \sqrt{25\cdot 7} + \sqrt{9\cdot 7}
|
-10,728 |
-\frac{1}{12 \cdot t + 48 \cdot (-1)} \cdot (t \cdot 36 + 96 \cdot (-1)) = \frac{1}{12} \cdot 12 \cdot (-\frac{1}{4 \cdot (-1) + t} \cdot (8 \cdot \left(-1\right) + 3 \cdot t))
|
36,277 |
z^2 + y\cdot z\cdot 2 + y^2 = (z + y)^2
|
14,609 |
1 + \tan{a} i = \tfrac{1}{\cos{a}}(i\sin{a} + \cos{a})
|
9,352 |
x_k = x_k\times 2 + \left(-1\right)
|
-2,745 |
\sqrt{10} \cdot 8 = \sqrt{10} \cdot (1 + 4 + 3)
|
8,532 |
n^3 - ((-1) + n) \left((-1) + n\right)^2 = 3 n n - 3 n + 1
|
-3,621 |
\frac{12}{z} = \frac{12}{z}
|
3,904 |
-2*d + 5 + \left(-1\right) = 4 - 2*d
|
-2,055 |
-\frac{\pi}{3} = 17/12*\pi - \dfrac{1}{4}*7*\pi
|
22,692 |
449 = 1 * 1 + 28*4^2
|
-18,089 |
13 = 48 + 35 \left(-1\right)
|
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