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math_formulas

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-1,669
-π\frac{1}{4}3 = π\dfrac{5}{6} - 19/12 π
27,072
\cos{y}*2 + 2\left(-1\right) = 1 - \cos^2{y}\Longrightarrow \cos^2{y} + 2\cos{y} + 3(-1) = 0
20,053
\lim_{n \to \infty}(2 + 10/n) = \lim_{n \to \infty} (n\cdot 2 + 10)/n
18,854
\frac{1/x * 1/x + 1}{-(\frac1x)^2 + 1} = \frac{x^2 + 1}{(-1) + x * x}
29,880
(3 + y)*(2*y + 1) = y * y*2 + y*7 + 3
-21,879
\frac16 + 8/12 = 1*2/\left(6*2\right) + 8/\left(12\right) = \frac{2}{12} + \frac{8}{12} = \left(2 + 8\right)/12 = 10/12
-4,701
\frac{1}{6 + y^2 + 5\cdot y}\cdot \left(-6\cdot y + 16\cdot (-1)\right) = -\frac{2}{y + 3} - \frac{4}{2 + y}
26,729
1 + (p + 1) \cdot ((-1) + p) = p^2
-18,464
60/45 = \dfrac{1}{3} 4
-13,726
\frac{1}{5 + (-1)} \cdot 16 = \frac{16}{4} = \frac14 \cdot 16 = 4
-2,699
\sqrt{3}\cdot 3 = (5 + 2 + 4\cdot \left(-1\right))\cdot \sqrt{3}
-7,735
\frac{1}{34}(10 + 130 i + 6i + 78 (-1)) = \tfrac{1}{34}(-68 + 136 i) = -2 + 4i
1,184
\gamma = \frac{\gamma}{π}\cdot π
24,994
h^2 - p^2 = (h - p) \cdot \left(p + h\right)
-9,305
66y^3 - 55y^2 = (2\cdot3\cdot11 \cdot y \cdot y \cdot y) - (5\cdot11 \cdot y \cdot y)
12,881
\sin(\pi \cdot l + x) = \sin(\pi \cdot l) \cdot \cos(x) + \cos(\pi \cdot l) \cdot \sin\left(x\right) = (-1)^l \cdot \sin(x)
-4,153
\frac{z^5}{z^3} = \tfrac{z\cdot z\cdot z\cdot z\cdot z}{z\cdot z\cdot z} = z \cdot z
28,682
\lim_{z \to 0^+} \sin{\dfrac1z} = \lim_{z \to \infty} \sin{z}
14,951
(-99)^2 + (-100) \cdot (-100) + (-101) \cdot (-101) = 101^2 + 99 \cdot 99 + 100^2
4,811
-1/4 + x^2 = (x - 1/2) (x + \tfrac{1}{2})
35,696
((-1) + y)\cdot (y \cdot y + y + 1) = (-1) + y^3
21,458
1/5!/2 = 1/240
18,481
\frac{1^2 + 1 + 2 \cdot (-1)}{2 + 3 - 2 \cdot 1^2} = \frac13 \cdot 0 = 0 \leq 0
-20,418
-\frac{18}{45} = -2/5*\frac{9}{9}
1,448
\frac32\cdot x = \vartheta rightarrow x = 2/3\cdot \vartheta
19,673
1 + 3 + 5 + \dotsm + x \cdot 2 + (-1) = x^2
25,622
(A^H)^2 = A^H \cdot A^H = (A^2)^H = A^H
-22,945
\dfrac{5*5}{5*6} = 25/30
253
\sin{1/12} = \sin(\frac{1}{3} - 1/4)
2,135
z^2\cdot 2 + 2 z + 2 = 2 z z + 2 z + 2
338
x = \tfrac{2x}{2} = (2x + 1)/2
31,693
987654321 - 8*123456789 = \frac{1}{9^2}*(1 + 8*\left(10^2 + 9*(-1)\right)) = 9
13,050
2! = 3!/3 = 3 \times 2/3 = 2
6,816
{n \choose k}\cdot k = n\cdot {\left(-1\right) + n \choose k + (-1)}
25,998
2 + \left(x + \left(-1\right)\right)^4 + (x + \left(-1\right))^2*3 = (x + \left(-1\right))^4 + x^2*3 - x*6 + 5
9,330
(\sqrt{a}*\sqrt{b})^2 = (\sqrt{b})^2*\sqrt{a} * \sqrt{a}
1,624
1 + 9\cdot z + z^2\cdot 28 + 36\cdot z \cdot z \cdot z + 16\cdot z^4 = \left(1 + 2\cdot z\right)\cdot (1 + 4\cdot z)\cdot (z + 1)\cdot \left(1 + z\cdot 2\right)
-20,382
\left(4 + 28 \cdot q\right)/(-12) = \frac{1}{-3} \cdot (7 \cdot q + 1) \cdot 4/4
-10,585
-\dfrac{7}{3\cdot y^2}\cdot \frac{3}{3} = -\frac{21}{y^2\cdot 9}
26,842
2 - \dfrac{2}{1 + l} = \frac{l\cdot 2}{1 + l}
27,626
\int_{-1}^3 e\,\text{d}j = \int\limits_{-5}^{-1} e\,\text{d}j
11,036
(1 + z)^{1/2} = \left((1 + z)^1\right)^{\frac{1}{2}}
-30,561
\dfrac{96}{48} = 48/24 = \dfrac{1}{12} \cdot 24 = 2
-22,907
\frac{15}{25} = \dfrac{3\cdot 5}{5\cdot 5}
14,330
45 (-1) + 10^{k + 2} + 3.1^{k + 1} + 50 = 10^{k + 1 + 1} + 3.1^{k + 1} + 5
-30,784
x*40 + 70 (-1) = \left(7(-1) + x*4\right)*10
36,677
yB = B = By
-1,456
\frac{(-2) \cdot 1/7}{\frac13 \cdot \left(-8\right)} = -2/7 \cdot (-3/8)
145
(2 \cdot 2 + 1^2) \cdot 2 = 10
3,977
\frac{1 - y^8}{-y^2 + 1} = y^6 + 1 + y^2 + y^4
-5,964
\frac33 \cdot \frac{1}{(s + 4 \cdot (-1)) \cdot (s + 9 \cdot (-1))} \cdot 3 = \frac{9}{(9 \cdot (-1) + s) \cdot \left(4 \cdot \left(-1\right) + s\right) \cdot 3}
-4,514
\tfrac{1}{3 + x^2 - 4x}(3x + 11 (-1)) = \tfrac{4}{x + (-1)} - \dfrac{1}{3(-1) + x}
23,545
1/2 + 1 - \tfrac{1}{1/2 + 1} = 5/6 > \frac12
31,494
26460 = 7^2 \cdot 2^2 \cdot 3 3^2 \cdot 5
2,348
\tfrac{1}{X^2} + X^2 = (X + 1/X)^2 + 2 \cdot (-1)
-8,961
94.8\% = \dfrac{94.8}{100}
36,902
0 = 32*(-1) + 32
-23,824
\frac{25}{3 + 2} = \dfrac{25}{5} = \frac{25}{5} = 5
5,527
\frac{1}{x + 3}(\frac{1}{2(-1) + x}40 + x*5 + 15) = 5 + \frac{40}{(x + 3) \left(2(-1) + x\right)}
-21,024
-50/20 = -\frac{5}{2}*\dfrac{10}{10}
-6,429
\frac{2}{(8 \cdot (-1) + q) \cdot 2} = \dfrac{1}{2 \cdot q + 16 \cdot \left(-1\right)} \cdot 2
-19,307
\dfrac{\dfrac{7}{8}}{1/7}\times 1 = 7/1\times \frac{7}{8}
2,141
( a, b)\times ( c, d) = ( a, b, 0)\times ( c, d, 0) = ( 0, 0, a\times d - b\times c)
35,306
3^2 = 1^3 + 2^3
-18,663
-3 = 9*(y + 4*(-1)) = 9*y + 36*(-1) = 9*y + 36*(-1)
9,398
a^T\cdot X\cdot b = (a^T\cdot X\cdot b)^T = b^T\cdot X^T\cdot a
15,265
{l \choose \theta} = {l \choose l - \theta}
24,222
(x^2)^2 + x^2 = 4\cdot x^2 \Rightarrow 0 = x^4 - x^2\cdot 3
-7,018
\frac{4}{35} = 2/5 \cdot 4/7 \cdot \dfrac36
6,859
(2*(-1) + 1)^2 + (0 + (-1))^2 + (0 + 2*(-1))^2 = 6
11,343
2\left(-1\right) + z^2 - z = \left(1 + z\right) (2(-1) + z)
1,314
N\cdot t_2/(t_1) = N\cdot t_1\cdot t_2/\left(t_1\right)/\left(t_1\right) = N\cdot t_2/\left(t_1\right)
1,404
x^3*5 + 20*x^2 - x*195 + 270 = (x + 2*(-1))*(x + 9)*(x + 3*\left(-1\right))*5
-25,231
d/dx \sqrt{x^3} = x \cdot \frac{3}{2}
5,548
\cos{X} \cdot \sin{X} \cdot 2 = \sin{2 \cdot X}
-22,353
q^2 + q\cdot 14 + 45 = \left(5 + q\right)\cdot (q + 9)
955
\frac{1/7}{1/4 \times \frac13} = 12/7
13,062
8984 = 19^3 + 5 \times 5 \times 5 + 10^3 + 10 \times 10 \times 10
1,186
(2\cdot \frac{1}{3}) \cdot (2\cdot \frac{1}{3}) + (2\cdot \frac23)^2 = \dfrac{20}{9} \gt 2
-3,891
\frac{30\cdot t}{18\cdot t^4}\cdot 1 = \frac{30}{18}\cdot \frac{t}{t^4}
8,644
2 \cdot \cos(0) \cdot \sin(π) = 0
5,849
\frac18 \cdot 5 = \frac{1}{1.6}
41,569
2\cdot \left(3 + 1\right) = 8
33,696
\sqrt{z} + \sqrt{y} = \sqrt{(\sqrt{z} + \sqrt{y}) * (\sqrt{z} + \sqrt{y})} = \sqrt{z + y + 2\sqrt{zy}}
2,233
\dfrac{1}{4}(4 - y^2) = 1 - y^2/4
9,715
12 - 2\cdot z^2 \geq 16 + z^2 - z\cdot 8 \Rightarrow 0 \geq 4 + 3\cdot z^2 - z\cdot 8
-14,680
534 = 89 + 92 + 91 + 97 + 84 + 81
-1,601
5/2\times \pi = 13/12\times \pi + \pi\times \frac{17}{12}
35,311
\dfrac{1}{A\cdot B} = 1/(B\cdot A) \neq \frac{1}{A\cdot B}
24,540
\binom{T + 1}{1 + l} = \binom{T}{l} + \binom{T}{1 + l}
34,735
7 = 5 + 31 + 19*\left(-1\right) + 17*(-1) + 11 + 7*\left(-1\right) + 3
13,448
\frac{1}{1 - 1 - x_\tau} = \frac{1}{x_\tau}
19,188
\frac{\text{d}}{\text{d}\delta} \operatorname{atan}(\delta) = \frac{1}{1 + \delta^2}
16,822
(\frac{dx}{dt})^2 = -e^x \cdot 4 \Rightarrow \frac{dx}{dt} = 2 \cdot e^{\dfrac12 \cdot x} \cdot i
-1,615
-\frac{\pi}{6} + 2 \pi = \pi*11/6
32,852
\frac{\text{d}}{\text{d}z} \sin^{-1}{z} = \frac{1}{(-z^2 + 1)^{1 / 2}}
24,415
(1 + i)!*\left(i + 1\right) + (i + 1)! = (i + 1 + 1)*(i + 1)!
10,854
\frac{10*8*6*7!}{10!} = 8*6/(8*9) = 2/3
33,868
0 - x*6 + 9*(q*x + Z) = 3 + q*9 \implies q*9 + 3 = 9*x*q - 6*x + 9*Z
5,281
|x + y + 2 \cdot (-1)| = |x + (-1) + y + (-1)| \leq |x + \left(-1\right)| + |y + (-1)|