id
int64 -30,985
55.9k
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stringlengths 5
437k
|
|---|---|
38,973
|
x\cdot 2 = \frac{3 \pi}{4} \Rightarrow x = \frac{1}{8} \pi\cdot 3
|
-15,321
|
\tfrac{1}{\frac{q^{10}}{n^2} n^2} = \tfrac{1}{n^2*\left(\frac{q^5}{n}\right)^2}
|
1,912
|
\frac{l!}{(l - v)!\cdot v!} = {l \choose v}
|
-10,526
|
\frac{1 + p}{p^3 \cdot 4} \cdot \frac{1}{4}4 = \frac{4p + 4}{16 p^3}
|
-7,509
|
\tfrac14 \cdot 17 = 34/8
|
11,866
|
x\times \lambda_g = x\times \lambda_g
|
3,923
|
w \in \mathbb{R}, x - y = w\Longrightarrow x = w + y
|
21,812
|
4(-1) + (2(-1) + z) * (2(-1) + z) = z^2 - 4z
|
16,911
|
3/5 \cdot \frac{1}{4} \cdot 2 = \tfrac{1}{10} \cdot 3
|
18
|
1^2+1^2=1*2\implies 2=2
|
-9,119
|
\dfrac{1}{100}*74.8 = 74.8\%
|
-20,482
|
\frac{-n \cdot 10 + 4 \cdot (-1)}{n \cdot 70 + 28} = \frac{1}{4 + 10 \cdot n} \cdot (10 \cdot n + 4) \cdot (-1/7)
|
9,064
|
\eta = 1/\eta = 1/\eta\cdot L^{-T}/L = \eta\cdot L^{-T}/L
|
-30,701
|
21\times (-1) - x\times 14 = -7\times (2\times x + 3)
|
27,985
|
|z + (-1)| = |1 - z| \geq |1| - |z| = 1 - |z| rightarrow |z| \geq \frac{3}{4}
|
13,408
|
\frac{b}{g} = b/g
|
8,046
|
1 + 8 \cdot \frac19 \cdot ((-1) + 10^{l + 1}) = \frac{1}{9} \cdot (8 \cdot 10^{l + 1} + 1)
|
7,110
|
1 - \frac{1}{1 + x^n} = \frac{1}{x^n + 1}*x^n
|
24,234
|
\frac{1}{(d + x) \cdot (x + h)} = \frac{1}{h - d} \cdot (-\frac{1}{h + x} + \frac{1}{d + x})
|
4,606
|
y*T/I = y*T/I
|
15,053
|
\dfrac{a^b}{a^d} = a^{-d + b}
|
-509
|
\frac{11}{12} \cdot \pi = -26 \cdot \pi + \pi \cdot 323/12
|
15,737
|
x^{3/2} = x^{\frac{1}{2}}*x
|
32,079
|
\dotsm^2 = \dotsm\cdot \dotsm
|
49,740
|
54/6=9
|
-2,690
|
25^{\frac{1}{2}}\cdot 7^{\frac{1}{2}} + 7^{\frac{1}{2}} = 5\cdot 7^{1 / 2} + 7^{\frac{1}{2}}
|
28,875
|
5/2 - \frac25 = \frac{21}{10}
|
-30,073
|
14 \cdot y + 6 \cdot y^5 + y \cdot y \cdot y \cdot 12 = \frac{\mathrm{d}}{\mathrm{d}y} \left(7 \cdot y^2 + y^6 + 3 \cdot y^4\right)
|
23,865
|
\cos^k{z} = \cos^k{z}
|
19,765
|
3 (-1) + 7 = 4
|
875
|
2 = A/x = \frac{A}{x \cdot U} \cdot \dfrac{U}{x} \cdot x = \dfrac{1}{x \cdot U} \cdot A \cdot |U|
|
-2,340
|
\frac{6}{11} - 4/11 = \frac{1}{11}*2
|
30,293
|
1365 = 19^2\cdot 3 + 16\cdot 19^0 + 14\cdot 19^1
|
21,618
|
\frac{y}{y + (-1)} = \frac{1}{y + \left(-1\right)}\cdot (y + (-1) + 1) = 1 + \frac{1}{y + (-1)}
|
10,361
|
x^2 + 3 - x^2 + 2\cdot x + 1 = x^2 - x^2 - 2\cdot x + 3 + \left(-1\right) = -2\cdot x + 2 = -2\cdot (x + (-1))
|
15,272
|
0 = B_4 - B_1*2 - 3*\frac{1}{5}*(2*B_1 - B_2) \Rightarrow B_4*5 - B_1*16 + 3*B_2 = 0
|
-20,058
|
\dfrac{1}{k + 9} \left(-6 k + 6 (-1)\right)*9/9 = \frac{1}{81 + 9 k} (-54 k + 54 (-1))
|
17,141
|
-h + e - f = e - f - h
|
18,100
|
\frac{y}{y^4 + 9} = \dfrac{1/9 \cdot y}{1 - -\frac{y^4}{9}}
|
19,466
|
P(A) = P(A)
|
23,800
|
\left\lceil{\frac{5}{(30/7)^{1/2}}}\right\rceil = 3
|
1,611
|
1/10 = \frac{8}{9} \cdot 9/10/8
|
-23,609
|
1/5 = 1/5 \cdot 2/2
|
-1,469
|
-\frac95*(-\dfrac79) = \frac{\frac19*(-7)}{(-5)*1/9}
|
-2,120
|
11/12 \times \pi + \tfrac{1}{12} \times 23 \times \pi = \frac{17}{6} \times \pi
|
-22,710
|
\tfrac{1}{49}\cdot 28 = 7\cdot 4/(7\cdot 7)
|
21,175
|
\frac{1}{g_1 g_2} = 1/(g_1 g_2)
|
23,039
|
z^2 + \frac{1}{z^2} = 2 (-1) + (\frac1z + z) (\frac1z + z)
|
8,890
|
mc = mc
|
32,760
|
b*g = (\sqrt{g*b})^2
|
24,690
|
\frac16 + 1/6 = \frac{1}{3}
|
17,222
|
\dfrac{1}{2} + 1/4 + \dfrac18 + \ldots + \frac{1}{2^k} = \dfrac{1}{2^k}*((-1) + 2^k)
|
-7,563
|
\frac{-i\cdot 9 + 9}{3 + 3\cdot i}\cdot \frac{3 - i\cdot 3}{-3\cdot i + 3} = \frac{9 - i\cdot 9}{3 + 3\cdot i}
|
-1,632
|
\frac{3}{2}\cdot \pi = \pi + \frac{1}{2}\cdot \pi
|
12,111
|
\sin\left(\pi - e - h - c\right) = \sin(e + h + c) = \sin\left(e + h\right) \cos(c) + \cos(e + h) \sin(c)
|
15,026
|
0 < \tfrac{e^{-1/z}}{z} = \frac{1}{z\cdot e^{\frac1z}} < 2\cdot z
|
2,088
|
(x + 1)\cdot \left(1 + x \cdot x - x\right) = 1 + x^3
|
23,102
|
s^2*s = s^3
|
35,767
|
10 + 6\cdot \sqrt{3} = 1 + 3\cdot \sqrt{3} + 9 + 3\cdot \sqrt{3} = 1 + 3\cdot \sqrt{3} + 3\cdot (\sqrt{3})^2 + (\sqrt{3})^3 = \left(1 + \sqrt{3}\right)^3
|
-11,580
|
-6 i - 9 + 1 = -8 - i*6
|
11,655
|
(-c a + a^2 + d d + c c - d a - c d) \left(a + d + c\right) = a^3 + d d d + c^3 - 3 d c a
|
-20,243
|
8/5 \dfrac{8 + 6q}{6q + 8} = \frac{64 + 48 q}{q\cdot 30 + 40}
|
21,537
|
2*\left(-b + a\right) = 2*a - 2*b
|
6,992
|
\dfrac{30}{12^5}\cdot 66 = 55/6912
|
16,569
|
\sin(\pi - t\cdot \pi) = \sin{\pi\cdot t}
|
-18,960
|
\frac192 = Z_t/(81 \pi)\cdot 81 \pi = Z_t
|
10,475
|
\cos(x \cdot t) = \cos(-t \cdot x)
|
976
|
a a + a b*2 + b^2 = (b + a) (b + a)
|
15,713
|
X \cdot X \cdot X - t^2 \cdot t = (X - t)\cdot (X^2 + t\cdot X + t^2)
|
4,795
|
-1.3 = (j + 10\cdot (-1))/2 \Rightarrow j = 7.4
|
33,797
|
5 \cdot 5 + 5^2 = 7^2 + 1 \cdot 1
|
4,195
|
\overline{e^{m\cdot x + i\cdot p}} = \overline{e^{m\cdot x}\cdot e^{i\cdot p}} = e^{m\cdot x}\cdot e^{-i\cdot p} = e^{m\cdot x - i\cdot p}
|
2,030
|
\frac{1}{x + 1}(x^2 + 2x + 2) = x + 1 + \frac{1}{1 + x}
|
-4,231
|
40/120\cdot y/y = 40\cdot y/\left(120\cdot y\right)
|
9,763
|
1/\left(g\cdot x\right) = 1/(x\cdot g)
|
-16,412
|
3\cdot (16\cdot 3)^{\frac{1}{2}} = 3\cdot 48^{1 / 2}
|
5,562
|
\frac{1}{4323} = 4322 \cdot 1/4323/4322
|
26,760
|
\dfrac{x}{c_3}\times 1/c_2\times \ldots^{-1}/A = x\times |c_2\times |c_3|\times \ldots|\times A
|
16,285
|
l = \dfrac{l!}{\left(\left(-1\right) + l\right)!}
|
-20,586
|
\frac{1}{3} \times 8 \times \frac{1}{2 + 9 \times n} \times \left(n \times 9 + 2\right) = \dfrac{16 + 72 \times n}{27 \times n + 6}
|
16,097
|
A^T*z*u = z*A^T*u
|
33,466
|
\frac{x^2}{x!} = \frac{1}{(x + \left(-1\right))!} + \frac{1}{(x + 2\cdot \left(-1\right))!}
|
14,409
|
a^l\cdot x = a^l\cdot x
|
27,613
|
2*\left(x + 1\right) = 2*x + 2
|
-19,072
|
1/2 = \frac{1}{49*\pi}*H_q*49*\pi = H_q
|
10,928
|
z^2 + z + 1 = (z + 2)\cdot \left(z + 2\right) = (z + (-1))\cdot (z + (-1))
|
17,914
|
2 \cdot (-1) + 2/3 \cdot q = 4 \cdot (q + 3 \cdot (-1))/6
|
39,838
|
\frac{n + 3}{n^2 + 3*(-1)} < \tfrac{n + 3}{n^2 + 9*(-1)} = \tfrac{n + 3}{(n + 3)*(n + 3*\left(-1\right))} = \frac{1}{n + 3*(-1)}
|
814
|
-z_1 * z_1*3 + z_1 z_2*10 - 3z_2^2 = (z_1 + z_2)^2 - (2z_1 - 2z_2)^2
|
31,778
|
17\times 16\times 15\times \dotsm\times 2 = 17!
|
49,984
|
\frac{1}{4} (k + 2)^4 = \frac14 (k + 1 + 1)^4 = \dfrac14 (k + 1)^4 + (k + 1)^2 + 1/4 + (k + 1)^3 + k + 1 + \frac12 (k + 1) (k + 1)
|
17,287
|
(-10 + 4\cdot \sqrt{10})/9 = -10/9 + \dfrac{\sqrt{10}\cdot 4}{9}
|
7,204
|
B^2 + (-1) = (B + 1)\cdot (B + (-1))
|
7,748
|
\frac1x \cdot 2 + 2 = \left(2 + x \cdot 2\right)/x
|
-182
|
\frac{1}{(8 + 4\cdot (-1))!}\cdot 8! = 8\cdot 7\cdot 6\cdot 5
|
21,644
|
(k\cdot 4 + \left(-1\right))^3 = 64 k^3 - 48 k^2 + k\cdot 12 + \left(-1\right)
|
18,225
|
1 = ((-1)^2)^{\dfrac12}
|
13,679
|
(4 + t^2 \cdot 4)^{1 / 2} = u \Rightarrow 4 \cdot t^2 + 4 = u \cdot u\wedge t^2 = \frac14 \cdot (u \cdot u + 4 \cdot \left(-1\right))
|
-26,576
|
2\times y^2 + 162\times (-1) = 2\times (y^2 + 81\times (-1)) = 2\times (y + 9)\times (y + 9\times (-1))
|
2,749
|
m = 5 \Rightarrow -1 = (-1)^m
|
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