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math_formulas

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-6,428
\frac{5}{4\cdot y + 20\cdot (-1)} = \frac{5}{(y + 5\cdot \left(-1\right))\cdot 4}
13,530
\frac12 \cdot (-k + n) + k = \frac12 \cdot (k + n)
1,303
\dfrac{2\tan{y}}{1 + \tan^2{y}} = \sin{2y}
-5,649
\frac{2}{2*(p + 10*(-1))} = \frac{1}{20*(-1) + p*2}*2
7,135
p/3 < 1 \implies 3 \gt p
21,058
\frac{f}{4} = f \cdot f/(f\cdot 4)
-3,070
(1 + 5 + 2) \cdot 3^{\frac{1}{2}} = 8 \cdot 3^{\frac{1}{2}}
1,218
\left(183 + 84\cdot (-1)\right)/3 = 33
16,697
40 + 2*10^2 - 16*10 = 80
19,340
\frac{720}{3 \cdot 2} \cdot 1 = {10 \choose 3}
7,901
C_2 C_1 = C_1 C_2 \Rightarrow e^{C_2} e^{C_1} = e^{C_2 + C_1}
4,901
5 = \frac{x + H + z}{z \cdot x \cdot H}\Longrightarrow H \cdot x \cdot z = 1
17,835
1 + k \cdot z + z = 1 + (k + 1) \cdot z \leq (1 + z)^k + z
-1,605
-\frac{\pi}{2} + \pi \cdot 7/6 = 2/3 \cdot \pi
-11,627
i\cdot 21 + 3 = 21 i - 9 + 12
8,008
1 + \frac{4}{(-1) + i} = \frac{i + 3}{i + \left(-1\right)}
-18,371
\frac{1}{49 + s^2 + s \times 14} \times (s \times s + 7 \times s) = \frac{s \times (s + 7)}{(s + 7) \times (s + 7)}
-860
0 + \frac{1}{10} 4 + 7/100 + \frac{5}{1000} + 2/10000 = \dfrac{4752}{10000}
-731
(e^{\dfrac{1}{12} 7 \pi i})^7 = e^{\pi i*7/12*7}
23,937
-\dfrac{20}{36} + 1 - \frac{1}{36} = \frac{15}{36}
14,841
\frac{1}{6}*(3^3 - 3*(2 * 2 * 2 + 2*(-1)) + 3*\left(-1\right)) = (27 + 18*(-1) + 3*(-1))/6 = 1
27,495
1 + 2^2 + 3^2 + \ldots*n^2 = n/6*(1 + n)*\left(1 + 2*n\right)
-17,424
84 = 39 + 45
10,433
\cos{\dfrac{2}{5} \cdot \pi} + \cos{4 \cdot \pi/5} = -1/2
31,119
\mathbb{E}(Y) = \mathbb{E}(s_H\cdot Y_1 + s_B\cdot Y_2) = s_H\cdot \mathbb{E}(Y_1) + s_B\cdot \mathbb{E}(Y_2)
909
\left(a + f\right)*(a - f) = a^2 - f^2
22,883
\tfrac{2}{15} = 2/15
31,002
\frac{(x + (-1))!}{\left(-x + x + (-1)\right)! \cdot x!} = \binom{x + (-1)}{x}
29,884
i\cdot b + a = b\cdot i + a
20,466
1/\left(1/(\dfrac{1}{1/25})\right) = 5^{-2*\left(-(-1)*(-1)\right)} = 5^2 = 25
15,574
b \cdot b + a \cdot a + 2\cdot a\cdot b = \left(a + b\right)^2
17,460
\frac{1}{h*d} = \frac{1}{h*d}
28,990
\frac{l!}{(l - D)! D!} = \binom{l}{D}
23,937
1 - \tfrac{1}{36} - 20/36 = 15/36
1,535
\frac{1}{u \cdot u} + u^2 = (u + \tfrac{1}{u})^2 + 2 \cdot (-1)
3,226
\log_W(g) = \log_e(g)/(\log_e(W))
-17,627
9(-1) + 32 = 23
-4,089
\frac{1}{y^5} \cdot y^3 \cdot 44/12 = \frac{44}{y^5 \cdot 12} \cdot y^3
36,432
7\cdot 17\cdot 23 = 2737
-19,390
\frac{3}{6\cdot \frac{1}{5}}\frac{1}{7} = 5/6\cdot \frac37
41,564
0.76 \cdot 0.76 + 0.65^2 = 1.0001
38,374
162 (-1) + 48 + 24 + 72 (-1) + 162 = 0
25,116
(f + h)^2 = h \times h + f^2 + f \times h \times 2
193
1 + h = \left(1 + \frac{1}{m}\right)^{\frac13} \implies (h + 1)^3 = 1 + 1/m
-26,391
x^n*x^m = x^{m + n}
-28,987
4*91.25 = 365
45,896
10!/5! = 10*9*8*7*6 = 30240
30,221
C_2 \cup C_1 \backslash C_2 = C_1 \Rightarrow \{C_2, C_1\}
-29,871
d/dz (5 \cdot z^4) = 5 \cdot \frac{d}{dz} z^4 = 5 \cdot 4 \cdot z \cdot z \cdot z = 20 \cdot z^3
17,965
(-160)^2 - 1 \times 22 \times 4 = 25512
-7,233
4/55 = 2/11 \cdot \frac{4}{10}
1,857
37.5 = \frac{1}{100}\cdot 15\cdot 250
-3,426
\sqrt{3}*3 = (4 + (-1))*\sqrt{3}
35,311
\frac{1}{E \cdot b} = \frac{1}{b \cdot E} \neq \frac{1}{E \cdot b}
253
\sin{\frac{1}{12}} = \sin(-1/4 + \frac13)
7,734
(-\sqrt{3}\cdot 2 - 1)\cdot \left(1 - \sqrt{3}\cdot 2\right) = 11
-17,037
2 = 2\cdot (-3\cdot s) + 2\cdot (-1) = -6\cdot s - 2 = -6\cdot s + 2\cdot (-1)
-5,143
\dfrac{0.54}{1000} = 0.54/1000
31,405
-k + n = -(k + (-1)) + n + (-1)
20,336
(f + e) v_1 + v_2 (f + e) = (v_1 + v_2) (e + f)
25,940
(-x + I)\cdot (I + x + x^2 + \dots + x^k) = -x^{1 + k} + I
26,023
6 = \frac{1}{2} \cdot (4 \cdot \left(-1\right) + 16)
-2,431
5^{1/2}*2 + 3*5^{1/2} = 5^{1/2}*9^{1/2} + 4^{1/2}*5^{1/2}
5,117
h*1/x/(h*1/x) = \dfrac{x}{h} \frac{h}{x}
-3,112
\sqrt{13}*4 - \sqrt{13} = \sqrt{13}*\sqrt{16} - \sqrt{13}
46,795
\frac{\partial}{\partial t} e^{-\int_0^t r \cdot s\,ds} = (e^{-\int_0^t r \cdot s\,ds}) \cdot \frac{\partial}{\partial t} (-\int\limits_0^t r \cdot s\,ds) = (e^{-\int_0^t r \cdot s\,ds}) \cdot \left(-r \cdot t\right) = -r \cdot t \cdot e^{-\int\limits_0^t r \cdot s\,ds}
-27,372
230 +{148}= 378
746
(-\frac12)^{\frac12} = \sqrt{-1/2}
-1,790
-\pi \cdot \dfrac53 + 4/3 \cdot \pi = -\pi/3
22,616
0 = x\times 2 \Rightarrow 0 = x
19,229
(519 + 89 \times \sqrt{34}) \times (-89 \times \sqrt{34} + 519) = 47
-7,817
\frac{i\cdot 21 + 1}{2\cdot i - 3} = \tfrac{i\cdot 21 + 1}{-3 + i\cdot 2}\cdot \dfrac{-3 - 2\cdot i}{-i\cdot 2 - 3}
-2,652
-5^{\frac{1}{2}} + 125^{\frac{1}{2}} + 20^{1 / 2} = -5^{1 / 2} + (25*5)^{1 / 2} + (4*5)^{\dfrac{1}{2}}
33,354
87091 + 4 (-1) = 87087
2,858
0 = \frac{1}{c} + \frac{1}{h} + \frac{1}{b}\Longrightarrow 0 = (hc + hb + bc)/(hcb)
631
\sqrt{(-3) \times (-3) + (-1)^2 + 2^2} = \sqrt{14}
24,578
\frac{1}{x^{1/2}*x^{\frac12}} = 1/x
-492
(e^{7*\pi*i/4})^6 = e^{6*\frac{i*\pi*7}{4}}
9,476
2^{\frac18\cdot (n + 1)} = 2^{1/8}\cdot 2^{n/8} \gt 2^{1/8}\cdot n
28,223
\frac{1 + x}{((-1) + x)^2} = \dfrac{x + (-1) + 2}{((-1) + x) \cdot ((-1) + x)}
21,662
1 = c\cdot h/\left(c\cdot h\right) = h\cdot \frac{\dfrac1c\cdot c}{h}
8,990
A_1 = \left\{\dots, 256, 129130\right\} \implies 128 = |A_1|
23,938
1 = (-1)\cdot (-1) = (y + \frac{1}{y})\cdot (y^2 + \dfrac{1}{y^2}) = y^3 + y + 1/y + \dfrac{1}{y \cdot y^2} = y^3 + (-1) + \frac{1}{y^3}
-7,658
\dfrac{22 \cdot i - 7}{2 + i \cdot 3} = \dfrac{1}{2 + 3 \cdot i} \cdot (-7 + i \cdot 22) \cdot \frac{-3 \cdot i + 2}{2 - 3 \cdot i}
-9,145
2 \cdot 3 \cdot 7 \cdot q \cdot q = 42 \cdot q^2
5,355
-\frac5w + 1 = \frac1w \cdot (5 \cdot (-1) + w)
13,197
e^{(C_1 + C_2) \cdot p} = e^{C_1 \cdot p} \cdot e^{C_2 \cdot p} = e^{C_2 \cdot p} \cdot e^{C_1 \cdot p}
23,572
qa + qx = (a + x) q
183
f_1 = \dfrac{1}{f_2 + z} \cdot (y + f_2) \Rightarrow y + f_2 = f_1 \cdot (z + f_2) = f_1 \cdot z + f_1 \cdot f_2
-22,835
\frac{108}{120} = \tfrac{9 \cdot 12}{12 \cdot 10}
1,021
e^{x + y} = e^{x}\cdot e^{y}
-26,542
100 - 9*z^2 = (10 - z*3)*(3*z + 10)
9,907
1/4 = 1/7 + \frac{1}{21} + \frac{1}{28} + \frac{1}{42}
-20,814
\frac{7}{7} \times (-s \times 5 + (-1))/5 = \frac{1}{35} \times (7 \times (-1) - s \times 35)
2,216
\left(a + b\right) \times (a - b) = -b^2 + a \times a
30,504
-q + 3\cdot (2\cdot e - 3\cdot q) = -10\cdot q + 6\cdot e
-1,101
((-9)\cdot 1/2)/(\frac{1}{7}\cdot 9) = \frac197 (-9/2)
27,340
k = k + (3 - k) \cdot 0
4,797
\left(e^x + (-1)\right) \cdot \frac{1}{(-1) + e^x} \cdot x = x
1,174
\frac1611 \pi = -\frac{\pi}{6} + \pi*2