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ddrg
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math_formulas

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-17,682
65 \cdot (-1) + 73 = 8
9,807
\frac{1}{A \times B} = \dfrac{1}{B \times A}
5,398
(2 + x)^{\frac{1}{2}} - x^{1 / 2} = \frac{1}{x^{\frac{1}{2}} + (x + 2)^{\dfrac{1}{2}}}\cdot 2
12,783
\left(x + (-1)\right)!/x! = \frac1x
-20,127
\dfrac99*\frac{1}{k*9}*(6*(-1) - 6*k) = \frac{1}{81*k}*\left(-k*54 + 54*(-1)\right)
18,138
1 + 2^{1 + 3^n} = 2^{3^n}\cdot 2 + 1
24,698
y^{1 / 2} * y^{1 / 2} = y
7,421
-7/6 + 7 = \frac{1}{6} \cdot 35
1,542
1/3 = \dfrac{1}{3} \cdot 2/2
-26,545
c^2 - d^2 = (d + c)\cdot (c - d)
3,297
2m^2 - 2m + 1 = m^2 + m^2 - 2m + 1 = m^2 + (m + (-1))^2
19,401
x + 4/3 x = 7/3 x
17,847
3 + 2 \cdot 12 = 2 \cdot 12 + 3
-4,285
\frac{6}{5} = \frac{1}{5} \cdot 6
15,932
-\int \sin{u}\,du + \sin{u}\cdot (u + (-1)) = (u + (-1))\cdot \sin{u} + \cos{u}
3,958
\frac{1}{24} 2 = \dfrac{2}{2 + 7 + 15}
-20,205
-\dfrac{5}{-5}*\frac173 = -\frac{15}{-35}
9,148
0 = Z\cdot H - Z\cdot H = \frac{Z\cdot B}{l_1} - B\cdot H/(l_2) = (Z\cdot B\cdot l_2 - l_1\cdot B\cdot H)/(l_2\cdot l_1)
15,985
\left(2^{m - n} + (-1)\right)\times 2^n = 2^m - 2^n
10,848
(5 + 14)/2 = 9.5
-5,907
\frac{1}{2(s + 3(-1))}5 \dfrac{(2(-1) + s) \cdot 3}{3(2\left(-1\right) + s)} = \tfrac{(s + 2(-1)) \cdot 15}{\left(2(-1) + s\right) (3(-1) + s) \cdot 6}
24,447
\sin{\frac12 \cdot 3 \cdot \pi} = -1 \lt 0
23,461
C \times D = C \times D
12,393
1 - x_2\cdot x_1 = 1 - x_1 + 1 - x_2 - (1 - x_2)\cdot (-x_1 + 1)
1,424
\pi/3 = -2\pi/3 + \pi
-10,719
-\frac{18}{48 \cdot (-1) + q \cdot 12} = -\frac{1}{4 \cdot q + 16 \cdot (-1)} \cdot 6 \cdot 3/3
-410
(e^{\pi \cdot i/3})^{20} = e^{20 \cdot \frac{\pi}{3} \cdot i}
-10,653
\frac{9}{p + 3} \cdot 15/15 = \frac{1}{45 + 15 \cdot p} \cdot 135
1,699
(-(3\times k + 1)) \times (-(3\times k + 1)) = (3\times k + 1)^2
-22,225
(z + 8)\cdot (6\cdot (-1) + z) = 48\cdot (-1) + z^2 + z\cdot 2
3,209
2^x = 3 \cdot j + 1 \implies (j + 1) \cdot 3 + 1 = 2^{x + 2}
28,788
\frac{1}{\cos{2\cdot y} + 1}\cdot \sin{y\cdot 2} = \tan{y}
4,454
-y^1 + z^1 = \left(-y + z\right)\cdot z^0\cdot y^0
34,953
5^0 + 2 \cdot 2^2 = 3^2
-20,119
\frac{1}{n \cdot 3 + 6} \cdot \left(20 + n \cdot 10\right) = \frac{10}{3} \cdot \frac{1}{2 + n} \cdot (2 + n)
31,650
\sum_{i=0}^n \binom{n}{i} = \sum_{i=0}^n \binom{n}{i}
-24,735
-\tfrac{60}{100} = -160/100 = -1.6
18,069
(x + c) (x - c) = x x - c^2 = x x + 1 - 1 + c^2
49,155
\left(\begin{cases} x^3 - x & \text{for }\: 0 = z \\z^3 - z & \text{for }\: x = 0 \end{cases} \implies z^3 + x^3 = 0\right) \implies x = -z
8,373
2 + q = 2 \cdot l \cdot q + 1 \Rightarrow (l \cdot 2 + (-1)) \cdot q = 1
-4,145
\frac{y}{y^4} = \tfrac{y}{yy y y} = \frac{1}{y * y^2}
10,134
|v_0| = (\frac{m}{m + 1} \cdot 2)^{\frac{1}{2}} \Rightarrow m = \frac{v_0^2}{-v_0^2 + 2}
3,224
\left(m^2 + m + 1/4\right)^{1 / 2} - \tfrac12 = ((m + 1/2) \cdot (m + 1/2))^{\tfrac{1}{2}} - 1/2 = m
5,583
y^{2000} = (y^3)^{666}*y^2 = (-1)^{666}*y^2 = y^2
-23,813
\tfrac{1}{3 + 9} \cdot 36 = 36/12 = 36/12 = 3
4,048
4 c + 8 (-1) = 4 (c + 2 (-1))
-27,384
620 + 10*\left(-1\right) = 610
17,601
x^{\frac{1}{r} \cdot p} = (x^p)^{\dfrac{1}{r}} = (x^p)^{\frac1r}
15,927
z^2/2\cdot 2 = z^2
36,646
15^m = \left(3 + 12\right)^m
76
x \cdot s + r \cdot x = x \cdot (r + s)
-20,517
-\dfrac{5}{z + 3 \cdot (-1)} \cdot \frac{1}{9} \cdot 9 = -\dfrac{45}{27 \cdot (-1) + 9 \cdot z}
26,333
100 = 33\cdot 3 + 3 + 3(-1) + 3/3
-22,714
\frac{40}{36} = 10*4/(4*9)
-3,990
4p^2 * p = 4p^2 * p
27,144
3/16 = \dfrac{1}{4^2} \cdot (2^2 - 1^2)
23,404
\left(1 + \frac1n\right)^j = \left(1 + \frac{1}{n}\right) \cdot (1 + 1/n)^{j + \left(-1\right)} \geq (1 + 1/n)^{j + (-1)}
15,822
y\cdot e^{t^2} = z + h \Rightarrow y = \frac{h}{e^{t^2}} + \frac{1}{e^{t^2}}\cdot z
23,913
\left(L - J = -x + M \Rightarrow L - M = J - x\right) \Rightarrow M - L = -J + x
35,138
\frac{y^3}{(y^2 + 1)^{\frac{5}{2}}} = -\frac{y}{(1 + y^2)^{5/2}} + \frac{1}{(y^2 + 1)^{\dfrac{1}{2} \cdot 3}} \cdot y
31,063
(4\cdot m + 10\cdot \left(-1\right))\cdot \left(m + (-1)\right) + 2\cdot (m + \left(-1\right)) = \left(4\cdot m + 8\cdot (-1)\right)\cdot (m + (-1)) = 4\cdot (m + 2\cdot (-1))\cdot (m + \left(-1\right))
29,276
45 + 29 \sqrt{2} = (\sqrt{2} + 3)^3
10,604
\left(1 - z \cdot z\right)^{\frac{1}{2}} = \sin(\arccos{z})
13,101
e = b \implies -e + b = 0
-28,952
2500 = 50^2
36,504
7777 = 2223*\left(-1\right) + 10^4
5,798
M*E * E = C_D*M^2 - C_D*E * E = C_x*M^2 - C_x*E^2 = C_x*M^2 - (C_D*C_x - C_D*E)^2
-9,467
-i\cdot 24 = -i\cdot 2\cdot 2\cdot 2\cdot 3
-17,680
20 = 3\left(-1\right) + 23
30
\dfrac{1}{100}Y*5 = Y/20
8,198
\mathbb{E}\left[e^V\right] = e^{\mathbb{E}\left[V\right]}
538
\frac{dg}{dx}\cdot i = \frac{dg}{dy}
2,219
A_t\cdot x_t = x_t\cdot A_t
-485
(e^{11\times i\times \pi/12})^{10} = e^{10\times \dfrac{1}{12}\times \pi\times i\times 11}
4,936
\left(-1\right) + \mathbb{E}(X) = \mathbb{E}((-1) + X)
19,959
\frac{1}{2n}=\frac{1}{6n}+\frac{2}{6n}=\frac{1}{3n}+\frac{1}{6n}
16,152
-h/b = \frac{1}{b} \times \left((-1) \times h\right) = \frac{h}{(-1) \times b}
-27,694
d/dz (-\cos\left(z\right)) = \sin(z)
15,481
z^2 + 1 = \left(42\cdot z^2 + 42\right)/42
26,356
3 \cdot 3 - 2\cdot 2^2 = 1
19,476
Q^6 - 2*Q^3 + 1 = (Q^3 + (-1))^2 = (Q + (-1))^6
-19,032
\frac{1}{45} 26 = G_t/\left(81 π\right)*81 π = G_t
-24,498
4 \cdot 5 + 8 \cdot \frac{1}{7} \cdot 42 = 4 \cdot 5 + 8 \cdot 6 = 20 + 8 \cdot 6 = 20 + 48 = 68
-8,091
\dfrac{1}{-5 - i} \cdot (-i \cdot 15 - 23) \cdot \dfrac{-5 + i}{-5 + i} = \tfrac{-23 - 15 \cdot i}{-5 - i}
-19,686
\frac{7*2}{9} = \tfrac{14}{9}
7,447
\sin(\theta)*\cos(\alpha) + \sin\left(\alpha\right)*\cos(\theta) = \sin(\theta + \alpha)
33,396
H \cdot K = K \cdot H
6,088
1 * 1 + 7 * 7 = 2*5^2
16,642
\frac{1}{{25 \choose 9}} = \dfrac{9!}{25!}\cdot 16!
-22,960
\dfrac{42}{30}= \dfrac{2\cdot21}{2\cdot15}= \dfrac{2\cdot 3\cdot7}{2\cdot 3\cdot5}= \dfrac{7}{5}
20,259
\left(0 = X*x*X^U \Rightarrow X*X^U*x^U = 0^U\right) \Rightarrow 0^U = x^U*X^U
5,707
\tan^3(\arctan x)= (\tan(\arctan x))^3= x^3
-12,867
5\cdot (-1) + 25 = 20
23,712
\frac{1}{10^{2\infty + 1}} = \frac{1}{10^{\infty}}
-7,923
\frac{1}{32} \times (80 + 48 \times i - 80 \times i + 48) = (128 - 32 \times i)/32 = 4 - i
31,755
|z \cdot z - 4 \cdot z - -3| = |z + 3 \cdot (-1)| \cdot |z + (-1)| \leq 3 \cdot |z + \left(-1\right)|
10,888
\dfrac{1}{(x + 2\cdot (-1))\cdot (z + 2\cdot (-1))}\cdot ((-5)\cdot (x - z)) = \frac{1}{\left(x + 2\cdot (-1)\right)\cdot (2\cdot (-1) + z)}\cdot (-\left(2\cdot (-1) + x\right)\cdot (z\cdot 4 + 3\cdot (-1)) + (z + 2\cdot \left(-1\right))\cdot (3\cdot \left(-1\right) + 4\cdot x))
-9,176
12 \left(-1\right) - 12 k = -k*2*2*3 - 2*2*3
-18,481
5 \cdot \alpha = 2 \cdot (3 \cdot \alpha + (-1)) = 6 \cdot \alpha + 2 \cdot \left(-1\right)
26,127
C H_1 + C H_2 = (H_1 + H_2) C