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ddrg
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math_formulas

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23,388
\frac{1/2\cdot 3}{3} = \frac{1}{3\cdot \dfrac{1}{3}\cdot 2}
-20,537
9/(-63) = -\frac{1}{7} (-9/(-9))
23,528
2 = -3*4 + 14
3,237
-z^2 + x \cdot x = \left(z + x\right) (-z + x)
21,427
y^k + 1 = y^k - -1 = (y - -1) \left(y^{k + (-1)} - y^{k + 2 (-1)} + \dotsm + 1\right)
736
2^{10 k} = (1000 + 24)^k = 1000^k + 24*1000^{k + (-1)} k
-20,071
\dfrac{1}{3} \cdot 4 \cdot \frac{y \cdot 8 + 9}{9 + y \cdot 8} = \frac{36 + y \cdot 32}{24 \cdot y + 27}
13,086
3 \cdot (-1) + \frac72 = 1/2
13,363
q_l*q_k = q_k*q_l
-20,139
\frac{7*\frac{1}{7}}{k + 8*(-1)} = \frac{7}{k*7 + 56*(-1)}
16,599
g + g = (g + g)^2 = g\cdot g + g\cdot g + g\cdot g + g\cdot g = g + g + g + g
-13,358
4 + (\dfrac{48}{8}) = 4 + (6) = 4 + 6 = 10
20,922
\tan(7.9) = \tfrac{1}{C*E}*160 \Rightarrow 160/\tan(7.9) = C*E
10,316
(-1) + \beta^9 = (\beta \cdot \beta \cdot \beta + (-1)) \cdot (\beta^6 + \beta^3 + 1)
19,293
8 = (-1/5 + 3) (-\frac{1}{7} + 3)
20,038
S^2 = \left(-S\right)^2
-6,293
\frac{1}{45 + 5\cdot x} = \frac{1}{(x + 9)\cdot 5}
3,251
b \cdot g + g \cdot d = (d + b) \cdot g
-3,654
\frac{64\cdot p^4}{72\cdot p^2} = 64/72\cdot \frac{1}{p \cdot p}\cdot p^4
51,170
\frac14\cdot 512 = 128
-16,986
1 = -z \cdot z - 8\cdot z + z + 8 = -z^2 - 8\cdot z + z + 8
19,921
0 = x^2 - b \cdot b = (x + b)\cdot \left(x - b\right)
4,105
3 \int\limits_0^{\frac{\pi}{2}} 1\,\mathrm{d}x = \int_0^{\dfrac{3 \pi}{2}} 1\,\mathrm{d}x
22,447
2 = \frac{1}{z}\cdot 2\Longrightarrow z = 1
3,676
X^4 - T = (X^2 - T^{1/2}) \times (X^2 + T^{\frac12}) = (X - T^{1/4}) \times (X + T^{\dfrac{1}{4}}) \times (X^2 + T^{\frac{1}{2}})
31,588
(\left(-1\right)^{\frac{1}{1} \cdot 2})^{1/6} = 1
32,863
{l \choose i} = \dfrac{l!}{(l - i)! \cdot i!}
18,939
720/(360\cdot 1/11) = 22
3,553
x \cdot x \cdot x + x^2 \cdot 3 + 3x + 1 = (x + 1)^3
36,919
-1 = (-1)*10 + 9
14,851
E(U^3) = E(U^2) E(U)
-6,453
\dfrac{4r + 4 + 4r - 32 + 16r}{4r^2 - 28r - 32} = \dfrac{24r - 28}{4r^2 - 28r - 32}
8,895
s = v\cdot (n - m) + f + j + k\cdot \left(d - v\right) \Rightarrow j = -f + s - (n - m)\cdot v - (d - v)\cdot k
31,241
e + y - e + y = e + y - e - y = e - e + y - y
19,927
x^2 + 2*x*h + h^2 = (x + h)^2
30,835
(2 + y) \cdot (2 + y) + 4\cdot (-1) = y^2 + y\cdot 4
13,417
xz = \left(x + (-1)\right) \left(z + (-1)\right) + 1 + x + (-1) + z + (-1)
19,901
\frac{1}{g^2} = \frac{1}{g} \cdot \frac{1}{g}
5,511
h'\cdot x\cdot h\cdot j = h\cdot j\cdot h'\cdot x
-22,383
6 + 2(-1) = 4
36,667
3^m - S_{m + (-1)} = 3^m - \dfrac12(3^m + (-1)) = \frac{1}{2}(3^m + 1) = S_{m + (-1)} + 1
11,895
(A + B)^2 = A^2 + 2 \cdot A \cdot B + B \cdot B
21,795
\dfrac{4}{2\cdot (2\cdot t + 1)} = \dfrac{1}{2\cdot t + 1}\cdot 2 = \frac{1}{t + 1} + \dfrac{1}{(t + 1)\cdot (2\cdot t + 1)}
-5,107
8.7 \times 10^0 = 8.7 \times 10^{2 - 2}
10,990
\frac12 \cdot \pi \cdot (4 \cdot x + 1) = 2 \cdot \pi \cdot x + \frac{\pi}{2}
-18,273
\frac{z \cdot 9 + z^2}{z^2 + 14 \cdot z + 45} = \frac{z \cdot (9 + z)}{(z + 9) \cdot (z + 5)}
21,515
E((Y - g)^2) = E((Y - E(Y) + E(Y) - g)^2) = E((Y - E(Y))^2) + (E(Y) - g) \cdot (E(Y) - g)
2,092
2^{k + (-1)}\cdot (2\cdot k + 2\cdot (-1)) = 2\cdot k\cdot 2^{k + (-1)} - \left(2^{12}\right)^{k + (-1)}\cdot \left(k + (-1)\right) = 2^k\cdot (k + (-1))
30,721
1 + q^2 + q^4 = (1 + q * q) * (1 + q * q) - q^2 = (1 + q + q^2) (1 - q + q^2)
-11,635
1 - i*8 = 4 + 3(-1) - 8i
30,871
y + y + y = 3\cdot y
-16,602
7 \cdot 16^{1 / 2} \cdot 5^{1 / 2} = 7 \cdot 4 \cdot 5^{\frac{1}{2}} = 28 \cdot 5^{1 / 2}
17,097
\binom{13}{4}\cdot \binom{2}{1}\cdot \binom{1}{1}\cdot \binom{3}{1}\cdot \binom{4}{1} = 17160
-20,115
8/8 \times \frac{1}{m \times (-2)} \times (m + 7) = \dfrac{1}{(-16) \times m} \times (m \times 8 + 56)
11,091
xzy = zxy
34,697
n/2 \leq l \implies -l + n \leq \frac{1}{2} \cdot n
-3,918
\frac{r^5 \cdot 66}{24 \cdot r^2} = \frac{1}{24} \cdot 66 \cdot \frac{r^5}{r^2}
13,804
\frac{1}{10^1}*\left(10 + (-1)\right)^{1 + \left(-1\right)}*\frac{1}{1!*\left(1 + (-1)\right)!}*1! = 1/10
6,119
6\cdot 10\cdot \frac{2}{3} = y\cdot 4/3 \Rightarrow y = \dfrac13
20,719
660 = \binom{5}{2}\cdot \binom{(-1) + 10 + 3}{3 + (-1)}
17,289
|u_i \cdot D \cdot D|^2 - |u \cdot D^2|^2 = (|D^2 \cdot u_i| - |D^2 \cdot u|) \cdot (|D^2 \cdot u_i| + |u \cdot D^2|)
-29,109
8*10^2*3/10 = 3/10*800
-20,087
\frac{7}{7} \times \frac{5 \times (-1) + x}{x \times 3 + 4} = \frac{1}{21 \times x + 28} \times (35 \times \left(-1\right) + 7 \times x)
15,955
4\cdot 1/9/180 = \frac{1}{405}
33,817
R\cdot a\cdot (v_1 + v_2) = R\cdot a\cdot v_1 + v_2\cdot R\cdot a
-10,781
-\frac{6}{q\cdot 25 + 20\cdot (-1)}\cdot 2/2 = -\frac{12}{40\cdot (-1) + q\cdot 50}
31,939
10^{\frac13} = 10^{\frac{1}{3}}
21,204
10000 + t\cdot 200 + t^2 = (100 + t)^2
8,569
2x = x + 1 - -x + 1
14,180
x = x^{q^h} \implies (x^{q^{(-1) + h}})^q = x
-19,503
9/8\cdot \dfrac59 = 1/9\cdot 5/(8\cdot 1/9)
8,612
uk := ku
26,644
(2\cdot 5\cdot x)^2 + 2\cdot 5\cdot x = 100\cdot x \cdot x + 10\cdot x = 10\cdot (10\cdot x^2 + x)
15,028
\dfrac12 \cdot ((-a + c)^2 + (a - b)^2 + (-c + b)^2) = -c \cdot a + a^2 + b^2 + c^2 - b \cdot a - b \cdot c
-5,924
\dfrac{n*7 + 12 (-1)}{n * n + 36 (-1)} = \dfrac{1}{36 (-1) + n * n}(n + 6 + n*3 + 18 (-1) + n*3)
-9,830
0.4 = \dfrac{1}{10}*4 = 2/5
13,873
e^{1/x} = 1 + \frac1x + \frac{1}{2\cdot x \cdot x} + \cdots > \frac{1}{2\cdot x^2}
7,962
\left\{\ldots, 2, 1, 4, 3\right\} = \mathbb{N}
-19,545
\frac83\cdot 7/4 = \frac{\frac{8}{3}}{\frac{1}{7}\cdot 4}\cdot 1
31,574
x + 1 + 2 = 13 \Rightarrow 10 = x
14,512
c\cdot (d\cdot a + a\cdot d) = (d\cdot a + a\cdot d)\cdot c
-24,283
\frac{72}{7 + 5} = \frac{72}{12} = \frac{72}{12} = 6
2,756
4 \cdot \sqrt{3} + 7 = \sqrt{7^2 + (-1)} + 7
7,038
1560 = 40 (-1) + 1600
-3,111
5 \cdot \sqrt{5} = \sqrt{5} \cdot (4 + 2 + (-1))
-22,201
72 \cdot (-1) + q^2 - q = (8 + q) \cdot \left(9 \cdot (-1) + q\right)
46,564
\sin{4\cdot \cos^2{\theta}} = \sin(2 + 2\cdot \cos{2\cdot \theta}) = \sin{2}\cdot \cos\left(2\cdot \cos{2\cdot \theta}\right) + \cos{2}\cdot \sin(2\cdot \cos{2\cdot \theta})
32,592
\cot{2x} = 1\Longrightarrow \tan{2x} = 1
-509
\frac{11}{12} \cdot \pi = \pi \cdot 323/12 - \pi \cdot 26
33,186
{n \choose (-1) + r} (-(r + (-1)) + n)/r = (-r + n + 1)/r {n \choose (-1) + r}
-19,799
0.01 \times (-180) = -\dfrac{180}{100} = -1.8
-3,470
\frac{5*9}{5*20} = 45/100
22,126
1 + \frac{1}{k + 1} = \dfrac{2 + k}{k + 1}
19,664
\binom{m}{1}\cdot c_l^{m + \left(-1\right)}\cdot c_{l + (-1)}\cdot a_m = c_{(-1) + l}\cdot c_l^{(-1) + m}\cdot a_m\cdot m
911
(x + (-1))^2 - 2*\left(x + (-1)\right) + (-1) = x * x - 2*x + 1 - 2*x + 2 + (-1) = x^2 - 4*x + 2
-8,309
0 = \frac{1}{-3}\cdot 0
-20,572
\frac{i + 3\cdot (-1)}{i + 3\cdot (-1)}\cdot (-\frac{7}{4}) = \dfrac{-7\cdot i + 21}{4\cdot i + 12\cdot \left(-1\right)}
18,670
n \cdot 2 = 4n - 2n
-9,941
-1^{-1} (-\frac{1}{5}) = \frac{1}{5}(\left(-1\right) \left(-1\right)) = 1/5
10,866
A + G + C = A + G + C = A + G + C