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math_formulas

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-4,493
\frac{9\cdot z + 21\cdot (-1)}{z^2 - z\cdot 5 + 4} = \frac{1}{(-1) + z}\cdot 4 + \frac{1}{z + 4\cdot (-1)}\cdot 5
-3,347
6^{1/2} \times 9^{1/2} + 6^{1/2} \times 25^{1/2} = 3 \times 6^{1/2} + 5 \times 6^{1/2}
-3,648
\frac{120 k^4}{k^3*144} = 120/144 \frac{k^4}{k^2 * k}
34,347
\binom{y + x}{2} = (x^2 + 2xy + y \cdot y - x - y)/2
40,200
e! = e! \cdot 2 = e!
4,067
3 - z*2 = y^2 + z^2 \Rightarrow 4 = (z + 1)^2 + y^2
-16,815
-6 = 9\cdot m^2 - 9\cdot m - 6\cdot 3\cdot m - -18 = 9\cdot m \cdot m - 9\cdot m - 18\cdot m + 18
-6,310
\frac{1}{10 \cdot (-1) + n} \cdot (n + 10 \cdot (-1)) \cdot \frac{1}{n + 1} \cdot 3 = \dfrac{(n + 10 \cdot \left(-1\right)) \cdot 3}{(n + 1) \cdot \left(n + 10 \cdot (-1)\right)}
31,137
91/216 = -\dfrac{1}{216}125 + 1
-20,464
\frac{(-10) \cdot s}{60 \cdot s} = -\dfrac{1}{6} \cdot \frac{10}{10 \cdot s} \cdot s
16,512
y + 4\cdot (-1) + 4 = y
-4,613
\tfrac{1}{4 + x} - \frac{1}{5 + x}*3 = \frac{7*(-1) - 2*x}{20 + x^2 + x*9}
15,293
x * x + 9 = 0 \Rightarrow x = 3i,-i*3
13,910
\frac{16}{3} = \frac{1}{12}16 + \frac{16}{4}
-6,058
\frac{1}{g \cdot 4 + 40 \cdot (-1)} \cdot 2 = \dfrac{2}{4 \cdot (10 \cdot (-1) + g)}
4,542
\frac{y}{x} = \frac{0 (-1) + y}{x + 0 (-1)}
19,331
\sqrt{\frac{3}{4}^2 + \frac{3}{4}^2} = \sqrt{\frac{18}{16}} > 1
35,693
\frac{1}{2 \cdot U^4 - 5 \cdot U \cdot U + 3} = \dfrac{1}{\left(2 \cdot U^2 + 3 \cdot (-1)\right) \cdot (U^2 + (-1))} = \frac{1}{(\sqrt{2} \cdot U - \sqrt{3}) \cdot \left(\sqrt{2} \cdot U + \sqrt{3}\right) \cdot (U + (-1)) \cdot (U + 1)}
26,158
2\cdot (-w + k) + 0 = 0 \implies k = w
29,493
\tfrac{x}{\sqrt{-x^2 + 1}} = \tan{\theta} \implies \arctan{\dfrac{1}{\sqrt{-x^2 + 1}}x} = \theta
17,848
-(10 - x_l) + 15 = 5 + x_l
-29,148
3\cdot 3 + (-1) = 8
3,199
x*\gamma*z = x*z = z = x*\gamma*z
-20,175
\dfrac{p*42 + 14*(-1)}{8 - 24*p} = \dfrac{-p*6 + 2}{2 - p*6}*(-\frac14*7)
10,481
1 + r \cdot r \cdot 3 + 3 \cdot r = -r^3 + (1 + r)^3
19,397
(a + x) \cdot (-a + x) = x^2 - a \cdot a
-12,494
-\frac{1}{-6.5} \cdot 58.5 = 9
18,564
-\frac{1}{7} + 1 - 2/7 = \frac47
23,259
5^2 + 5 \cdot 25 + 25 \cdot 25 = 25 \cdot (1^2 + 5 + 5 \cdot 5) = 25 \cdot 31
-675
\left(e^{19 i\pi/12}\right)^{15} = e^{15 \frac{19}{12}\pi i}
-8,085
\frac{2 - 8 \cdot i}{3 + 5 \cdot i} = \frac{-8 \cdot i + 2}{3 + 5 \cdot i} \cdot \frac{-i \cdot 5 + 3}{3 - 5 \cdot i}
27,176
\binom{x}{j} = \frac{x!}{j! \times (x - j)!} = \binom{x}{x - j}
-10,557
\dfrac{1}{y*75}*\left(30*(-1) + y*5\right) = \frac55*\frac{1}{15*y}*(6*\left(-1\right) + y)
-13,440
\frac{40}{3 + 1} = \dfrac{40}{4} = \frac14 \cdot 40 = 10
21,958
1/(x*b) = 1/(b*x)
21,776
(u + x) I = uI + xI
-6,679
8/100 + \frac{1}{10}*9 = \frac{1}{100}*90 + \dfrac{1}{100}*8
6,362
\dfrac{1}{l + (-1)} - 1/l = \dfrac{1}{l \cdot ((-1) + l)}
19,543
e^{Q_2 + Q_1} = e^{Q_1}\cdot e^{Q_2}
-4,553
\frac{4}{4 \cdot (-1) + y} + \frac{1}{y + 2 \cdot (-1)} \cdot 3 = \dfrac{1}{y \cdot y - y \cdot 6 + 8} \cdot (20 \cdot (-1) + y \cdot 7)
15,014
z_{m + 1} - z_m = \frac{z^2 - z^2}{z_{m + 1} + z_m} = \frac{z_m + (-1)}{z_{m + 1} + z_m}
16,915
\cos((-y + \pi)/2) = \sin(y/2)
8,385
(\frac{1}{2}*3)^3/3 = 9/8
28,103
\sin{z} = \frac{1}{2 \cdot i} \cdot (e^{i \cdot z} - e^{-i \cdot z}) \cdot \cos{z} = (e^{i \cdot z} + e^{-i \cdot z})/2
15,152
e^{\pi/2} = 4.8104 \cdot \dots \approx 110^{\frac{1}{3}} = 4.791
10,565
(-1) + x^4 = \left((-1) + x\right) \times \left(1 + x\right) \times (x^2 + 1)
48,009
\sqrt{5 \cdot 5} = 5 = |5|
24,236
B \setminus Z + x = B \cap Z + x^c = B \cap Z^c + x
19,155
1/(\frac{1}{a}) = \dfrac{1}{1/a} = a
-4,555
(z + 3)\cdot (5\cdot (-1) + z) = 15\cdot (-1) + z^2 - z\cdot 2
-1,163
5/4 (-5/1) = 1/4 \cdot 5/(1/5 (-1))
160
\frac{18!}{3!*5!*10!} = 2450448
-2,142
\pi\cdot \frac{5}{3} = 7/6\cdot \pi + \pi/2
-4,026
\dfrac{1}{3} \times y^2 = y^2/3
9,680
\frac{48^2}{17^2}\cdot (34^2 - y^2) = (95 - y)^2 = 95^2 - 190\cdot y + y^2
20,995
-\sin{-y} \cdot (-1) = \sin{-y} = -\sin{y}
-4,303
g\cdot \frac32 = \frac{3}{2}\cdot g
-2,089
\pi\cdot \dfrac{17}{12} + 4/3\cdot \pi = \pi\cdot 11/4
17,120
\tfrac{1}{X^2 + X \cdot f + f^2} = \dfrac{X - f}{(X - f) \cdot (X^2 + X \cdot f + f \cdot f)} = \frac{X - f}{X^3 - f^3}
-17,976
43 = 20 + 23
4,180
l = x\cdot a \implies l/a = x
1,335
\frac{1}{y^M} = y^{-M}
28,005
\lim_{m \to \infty} z_m = a \Rightarrow \lim_{m \to \infty} |z_m| = |a|
1,246
\sin(-z)/\left((-1)*z\right) = \sin\left(z\right)/z
8,053
\tan\left(\arctan\left(x\right)\right) = x
36,138
30^2 - 24^2 = 900 + 576 (-1) = 324 = 4 \cdot 81
14,916
(s^k + (-1))! = 1 \cdot 2 \cdot 3 \cdot \dots \cdot \dots \cdot \left(s^k + (-1)\right)
-23,111
-7/2 = -\frac{1}{4} \cdot 7 \cdot 2
8,256
\frac{1}{(-1) + 2}(4(-1) + 30) = 26
-29,370
(7 + z) \cdot (7 - z) = 7^2 - z \cdot z = 49 - z^2
16,930
2*(1 + \frac{1}{17}) = \frac{35}{17} < 32/15
4,347
4 \cdot z = 4 \cdot z + 1 = z + z + \frac14 + z + \frac24 + z + 3/4
27,068
(-1) + G^{12} = (1 + G^6) (G^6 + \left(-1\right))
2,076
l_2^2 - l_1^2 = (-l_1 + l_2) \cdot (l_1 + l_2)
16,138
\frac{x^2}{x^2 \cdot x} = \frac1x
1,887
x = -2 \cdot x \cdot 7 + 5 \cdot x \cdot 3
-27,654
3/2 + 5/2 + 2\cdot \left(-1\right) = 4 + 2\cdot \left(-1\right) = 2
3,190
\left(1 + 3^4\right)*(3^2 + 1)*(\left(-1\right) + 3^2) = (-1) + 3^{2^3}
-20,892
\frac{5}{5}\cdot \left(-\dfrac65\right) = -30/25
-1,642
\frac{7}{4}\pi - \frac{3}{2}\pi = \frac{1}{4}\pi
-26,249
2 = De^{\left(-3\right)*0} = D
-20,582
4/4\cdot \frac{(-1) + q}{10\cdot (-1) - q} = \dfrac{q\cdot 4 + 4\cdot (-1)}{-4\cdot q + 40\cdot (-1)}
21,775
\left(x + (-1)\right)! \times (x + 1)! = \frac{x + 1}{x + (-1)} \times x! \times x! > x! \times x!
26,847
0 = b_y + b_z*c_y \Rightarrow -\frac{1}{b_z}*b_y = c_y
-12,020
3/5 = \dfrac{s}{6\cdot π}\cdot 6\cdot π = s
-5,306
24.0 \cdot 10^1 = 10^{-1 + 2} \cdot 24
-7,381
\frac{1}{91} \cdot 10 = 5/14 \cdot \frac{4}{13}
2,703
\left(5*(-1) + x \geq 0\Longrightarrow x + 5*(-1) = 1\right)\Longrightarrow x = 6
-19,503
9/8 \cdot 5/9 = \frac{1/9 \cdot 5}{1/9 \cdot 8}
10,951
t - s + 1 = -\binom{s}{2} + \binom{t + 1}{2} + \binom{s + (-1)}{2} - \binom{t}{2}
-10,383
-\dfrac{40}{a^2 \cdot 40} = -\frac{8}{8 \cdot a^2} \cdot 5/5
11,108
3^x\cdot 3^5 = 3^{5 + x}
-16,463
4 \cdot (9 \cdot 13)^{1 / 2} = 4 \cdot 117^{\frac{1}{2}}
6,822
2\cdot n = n\cdot 3 - n
-6,775
12 \cdot 3 \cdot 12 = 432
-20,729
-\frac57*\frac{10*z + 9}{z*10 + 9} = \frac{1}{z*70 + 63}*(45*(-1) - z*50)
47,602
2^z + 2^z = 2*2^z = 2^{z + 1}
9,772
y_l - x_l = 0\Longrightarrow y_l = x_l
11,918
(S^{1/2}\cdot T^{\frac12})^2 = S\cdot T
19,853
\dfrac{j^2}{j!} = \frac{j}{\left(j + \left(-1\right)\right)!} = \dfrac{1}{\left(j + 2 \cdot (-1)\right)!} + \frac{1}{(j + \left(-1\right))!}