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math_formulas

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10,931
\sin\left(\dfrac{21 π}{2} - π*2/2\right) = \sin(19 π/2)
14,477
z = 5 \Rightarrow 25 = z^2
18,509
3\cdot \sqrt{2} + 1 = 4 - 2\cdot \sqrt{2} - -5\cdot \sqrt{2} + 3
13,208
0 = w/3 + x \Rightarrow x = -w/3
23,375
(3 + x)*\left(x + 5*(-1)\right) = x^2 + 3*x - 5*x + 15*(-1)
20,775
\binom{52}{25} = \dfrac{1}{25! \cdot 27!} \cdot 52! = 477551179875952
-21,031
\frac187 \left(-7/(-7)\right) = -\dfrac{49}{-56}
716
x = 2*2x^2 = 8x^4
50,169
51 = 3*17
-2,401
(-5)^3 = (-5) \times (-5) \times (-5) = 25 \times \left(-5\right) = -125
-15,212
\frac{1}{m^{16} \cdot \frac{1}{m^5 \cdot r^5}} = \dfrac{1}{\tfrac{1}{m^5 \cdot r^5} \cdot m^{16}}
-2,225
\dfrac{3}{17} = \tfrac{1}{17} \cdot 9 - 6/17
-2,651
6*\sqrt{7} = (5 + 1)*\sqrt{7}
-18,468
b + 6 = 5 \cdot \left(5 \cdot b + 8 \cdot (-1)\right) = 25 \cdot b + 40 \cdot \left(-1\right)
8,652
\frac{5}{x^4} - \frac{5}{x^2} = \frac{5}{x^4}\cdot \left(1 - x \cdot x\right) \gt \frac{15}{4\cdot x^4}
-8,701
\frac{8}{6} - 5/4 = 8*2/(6*2) - 5*3/(4*3) = \frac{16}{12} - \frac{1}{12}*15 = \frac{1}{12}*(16 + 15*(-1)) = 1/12
28,046
\dfrac{(2 + x)^3 + 8*(-1)}{2 + x + 2*\left(-1\right)} = \frac{1}{x}*(12*x + 6*x^2 + x^3) = 12 + 6*x + x^2
5,938
4 - (-b + 1)*4 = 4*b
15,070
2 \cdot \left(-1\right) + 34 = 32
3,018
\frac12 \cdot 160 = 20 \cdot 4 = 80
28,591
\dfrac{1}{-\frac1g + \dfrac{1}{-1/f + g}} = -g + g f g
41,902
\frac{-2}{16}=-\frac{1}{8}
14,874
\frac{\partial}{\partial x} \left(a^2\cdot x^4\right) = a \cdot a\cdot 4\cdot x^3
14,520
\sqrt{(\cos(x) + (-1))^2 + \sin^2(x)} = \sqrt{2 - 2\cdot \cos(x)} = 2\cdot \sin\left(x/2\right) \lt x
25,233
\sin(z\cdot 2)\cdot z\cdot 2 + 2\cdot z^2\cdot \cos(z\cdot 2) = \frac{d}{dz} \left(z \cdot z\cdot \sin(2\cdot z)\right)
28,491
\frac{1}{y*(y + (-1))} = -\tfrac1y + \frac{1}{y + (-1)}
1,909
(n + 1)^2 \cdot 3 = n \cdot 4 + 3 + 3 \cdot n \cdot n - n \cdot 2 + 1 + n \cdot 4 + 1
13,018
2*\lambda^2 - \lambda + 3*(-1) = (\lambda + 1)*2*(\lambda + 3*(-1)) = 2*(\lambda + 1)*(\lambda + 3*\left(-1\right))
44,044
\frac11 = 1
32,991
1! \cdot 2 = 2
-26,140
3 \cdot 3^3 - 2 \cdot 3 \cdot 3 + 9 \cdot 3 - 3 \cdot 6^3 - 2 \cdot 6^2 + 9 \cdot 6 = 90 + 630 \cdot \left(-1\right) = -540
-7,423
1/(3\cdot 3) = \frac{1}{9}
413
\frac{1}{16^{1 / 2}}6^{1 / 2} = 6^{1 / 2}/4
38,090
9800*\frac{28}{3} = 274400/3
35,138
-\frac{1}{(1 + x^2)^{\frac{1}{2}5}}x + \dfrac{x}{(1 + x * x)^{3/2}} = \frac{1}{(1 + x^2)^{5/2}}x^3
-6,702
1/100 + 20/100 = 2/10 + 1/100
19,423
a - t^3 + a^3 = t rightarrow (a - t)\cdot (a^2 + t\cdot a + t \cdot t) + a - t = 0
-26,152
2\cdot 16^{\frac32} - 2\cdot 4^{\tfrac{3}{2}} = 128 + 16\cdot \left(-1\right) = 112
6,904
6 + k\cdot 2\cdot 3\cdot 5\cdot 7 = 6 + 210\cdot k
14,033
x + 2 \cdot (-x + n) = 2 \cdot n - x
36,082
\frac{9}{16} = \left(3/4\right)^2
26,080
B/A = \frac{B}{A}\cdot 1 = \tfrac{B}{A}\cdot 1 = B/A
37,432
\frac{1}{4} 3 = \frac34
-20,814
(-r\cdot 35 + 7\cdot \left(-1\right))/35 = \dfrac15\cdot (-r\cdot 5 + (-1))\cdot \frac{1}{7}\cdot 7
28,660
\frac{1}{x^{1/2} + 2} = \tfrac{1}{4 - x}*2 - \dfrac{1}{-x + 4}*x^{1/2}
17,799
\left((-1) + k\right)/2 + 2 = \frac{1}{2}*(k + 3)
32,486
\tan(\left((-1) \cdot π\right)/4) = -1
1,711
\frac{5}{5 + 4}\cdot \dfrac{6}{6 + 3} = \frac{1}{81}\cdot 30 \approx 0.37
34,879
\dfrac{1}{4} \cdot \left(f - c\right) = \frac{f}{4} - \frac{c}{4}
-23,194
-1/2 \cdot 8 = -4
18,819
c \cdot h = -c^2/2 + \frac{1}{2} \cdot (c + h) \cdot (c + h) - h^2/2
34,735
5 + 31 + 19 \times (-1) + 17 \times (-1) + 11 + 7 \times (-1) + 3 = 7
23,952
{m \choose m - c} = {m \choose c}
-8,549
2/4 - 2/6 = \tfrac{2*3}{4*3} - 2*2/(6*2) = 6/12 - \frac{4}{12} = \frac{1}{12}\left(6 + 4(-1)\right) = 2/12
-4,283
\frac{54\cdot s^5}{s\cdot 45} = \frac{54}{45}\cdot \frac1s\cdot s^5
4,042
\left((1/u)^2 + 1\right)^{1/2} \cdot u = (((\dfrac{1}{u}) \cdot (\dfrac{1}{u}) + 1) \cdot u^2)^{1/2} = (1 + u^2)^{1/2}
23,627
(-(k + \left(-1\right)) + N) \times \left(-(k + (-1)) + N + 1\right)/2 = \frac{1}{2} \times (2 + N - k) \times (1 + N - k)
29,748
99 \cdot 100/2 = 4950
-3,651
8/9 \cdot q^2 = \frac{q^2}{9} \cdot 8
8,544
\left(x + (-1)\right)*(x * x - x*2 + \left(-1\right)) = 1 + x^3 - 3*x^2 + x
5,137
-Q^2 + X^2 = (X + Q) \cdot (-Q + X)
24,612
\frac{5^{\frac13} \omega}{5^{\frac{1}{3}}}1 = \omega
2,960
\sqrt{5} + 2 = -(2\cdot (-1) - \sqrt{5})
15,085
\|x - D\| \leq \|x - D\|^3 \implies D = x
-9,152
-q^3*9 = -q*q*3*3*q
-18,665
2n + 2 = 6(n + 3) = 6n + 18
-6,696
\frac{1}{100} + \frac{9}{10} = \frac{90}{100} + 1/100
26,570
-(17 - \sqrt{34} \cdot 3) \cdot (\sqrt{34} \cdot 3 + 17) = 17
7,969
b + \frac12 \cdot \left(-b + a\right) = \frac{1}{2} \cdot (a + b)
3,465
0 = (x + y + z)^2 = 1 + 2*\left(x*y + x*z + y*z\right)
22,324
\tfrac{n}{n + (-1)} = \frac{n + (-1)}{n + \left(-1\right)} + \frac{1}{n + (-1)} = 1 + \frac{1}{n + (-1)}
-26,434
\frac17*64 = -16/7*(-4)
28,991
\sin{\chi} = \sin(\pi - \chi)
26,154
\frac{\partial}{\partial z} z^{l\cdot 2 + 1} = z^{2\cdot l}\cdot \left(2\cdot l + 1\right)
262
3\cdot x^2 \cdot x - 3\cdot x + 9 = 3\cdot (x^3 - x + 3) = 3\cdot \left(x^2 + f\cdot x + d\right)\cdot (x + c) = x^3 + (c + f)\cdot x^2 + \left(f\cdot c + d\right)\cdot x + d\cdot c
-1,795
\pi/2 + \pi \cdot 7/12 = \pi \cdot 13/12
12,024
\dfrac{-k + n}{1 + k} {n \choose k} = {n \choose k + 1}
6,635
\sin(\frac{1}{3} \cdot \pi) = \sqrt{3}/2
23,476
e^{\dfrac14 \cdot 3 \cdot π \cdot i} \cdot e^{π \cdot i/4} = e^{π \cdot i} = -1
29,461
A^6 = (A^2 + 2 \times A) \times (A^2 + 2 \times A) = A^4 + 4 \times A^3 + 4 \times A^2 = A^3 + 2 \times A^2 + 4 \times A^2 + 8 \times A + 4 \times A^2 = 11 \times A^2 + 10 \times A
4,544
y \cdot (n \cdot p_2 + d \cdot n \cdot p_1) = n \cdot p_1 \cdot y \cdot d + y \cdot p_2 \cdot n
26,323
(z^2 + x^2 + x \cdot z) \cdot (x^2 - z \cdot x + z^2) = z^4 + x^4 + x^2 \cdot z^2
34,243
Q^c^k = Q^1 \dotsm Q^k
-11,362
\left(x + a\right)^2 = (x + a) \cdot \left(x + a\right) = x^2 + 2 \cdot a \cdot x + a \cdot a
238
8^{2 \cdot n} \cdot 2^{4 \cdot n} = (64 \cdot 16)^n = 1024^n
-5,569
\frac{3 r}{(6 + r) \left(r + 2 (-1)\right)} = \dfrac{r}{12 (-1) + r^2 + 4 r} 3
5,712
\left(y = -x \cdot 3 + 4 \implies -x \cdot 3 = y + 4 \cdot (-1)\right) \implies x = \left(y + 4 \cdot (-1)\right)/\left(-3\right)
22,093
93.5 = 0.4 \cdot (0 + 95 + 0 \cdot (-1)) + 0.1 \cdot (95 + 0 \cdot (-1) + 5) + 0.4 \cdot \left(0 + 95 + 5 \cdot (-1)\right) + 0.1 \cdot \left(5 + 95 + 5 \cdot \left(-1\right)\right)
-20,294
4/4*\frac{2 + 2*y}{8 - 10*y} = \frac{1}{-40*y + 32}*(8*y + 8)
49,401
\frac{1}{\sqrt{95} + 9 \cdot \left(-1\right)} = (\sqrt{95} + 9)/14 = 1 + \left(\sqrt{95} + 5 \cdot \left(-1\right)\right)/14
29,036
\frac{1}{6} = 3/18 = \frac{1}{18} + 2/18 = \frac19 + \dfrac{1}{18}
16,144
\dfrac{1}{2} \cdot (\frac{\pi}{2} - \dfrac{\pi}{2}) = 0
10,951
p - x + 1 = \binom{p + 1}{2} + \binom{x + (-1)}{2} - \binom{p}{2} - \binom{x}{2}
-9,130
27 \left(-1\right) + y*15 = -3*3*3 + y*3*5
-10,008
0.01\cdot \left(-88\right) = -\frac{88}{100} = -22/25
478
4 = -F*2/5 + F rightarrow 20/3 = F
12,463
2^9*\cos(\frac{2*\pi}{3}) = -2^8
941
exp(x + z) = exp(x)*exp(z)
11,036
((1 + y)^1)^{1/2} = (1 + y)^{\frac{1}{2}}
-10,383
-\frac{1}{40\cdot a \cdot a}\cdot 40 = \frac15\cdot 5\cdot (-\frac{1}{a^2\cdot 8}\cdot 8)