id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
33,603 |
|(c + f\cdot i)^2| = |c \cdot c - f \cdot f + 2\cdot c\cdot f\cdot i| = \sqrt{(c^2 - f^2)^2 + 4\cdot c^2\cdot f^2} = c^2 + f \cdot f
|
-3,560 |
\frac{\frac{3}{4}}{z^3}\cdot 1 = \frac{3}{z \cdot z^2\cdot 4}
|
16,340 |
x^8 = x^2 \cdot \left(x^6 + 1\right) - x^2
|
19,636 |
(-1) + z^4 = (z + (-1)) (z^3 + z^2 + z + 1)
|
-3,483 |
\dfrac{1}{100} 5 = 0.05
|
-13,532 |
\dfrac{1}{5 + 6}\times 22 = 22/11 = 22/11 = 2
|
17,839 |
(c^2 + c*d + d * d)/a*\cdots*\cdots = \frac{1}{c - d}*a^2
|
34,366 |
\tfrac12 \cdot \left(6 + (-1)\right) \cdot (6 + 2 \cdot \left(-1\right)) = 10
|
-20,213 |
(54 (-1) + 90 z)/81 = \frac99 \frac19(10 z + 6(-1))
|
-20,914 |
5/5 \cdot \frac{-x \cdot 6 + 9}{\left(-5\right) \cdot x} = \frac{1}{x \cdot \left(-25\right)} \cdot (-30 \cdot x + 45)
|
846 |
\frac{1}{1 - x} + (-1) = \frac{1 - 1 - x}{1 - x} = \dfrac{1}{1 - x}\cdot x
|
19,380 |
{D \choose k} = {D \choose -k + D}
|
-2,015 |
\frac{23}{12} \pi - \frac{5}{12} \pi = \pi \dfrac32
|
-10,580 |
-\frac{60}{a^3 \cdot 300} = \frac{20}{20} \cdot (-\frac{1}{15 \cdot a \cdot a \cdot a} \cdot 3)
|
17,614 |
\cos(z_1 + iz_2) = \cos(z_1) \cos(iz_2) - \sin\left(z_1\right) \sin(iz_2) = \cos(z_1) \cosh\left(z_2\right) - i\sin(z_1) \sinh(z_2)
|
19,661 |
0 = c + yb\Longrightarrow y = -c/b
|
-5,879 |
\frac{1}{(x + 9)\cdot (x + 8)}\cdot (3\cdot (-1) + 6\cdot (9 + x) - (8 + x)\cdot 3) = \dfrac{6}{(9 + x)\cdot (x + 8)}\cdot \left(x + 9\right) - \frac{\left(x + 8\right)\cdot 3}{(9 + x)\cdot \left(x + 8\right)} - \frac{3}{\left(9 + x\right)\cdot (8 + x)}
|
36,937 |
0 = -y + 3 - 2*x\Longrightarrow y = 3 - 2*x
|
9,678 |
d\cdot c_2 = c_2\cdot d
|
7 |
\mathbb{E}[X_1] - \mathbb{E}[X_2] = \mathbb{E}[X_1 - X_2]
|
21,196 |
A\cdot D = x \Rightarrow x = D\cdot A
|
9,524 |
\frac{1}{1 - y} = -\tfrac{1}{y + \left(-1\right)}
|
5,602 |
e^{b*x} = \frac{1 + \dfrac{b}{2}*x}{1 - \frac{b}{2}*x} = \frac{1}{2 - b*x}*(2 + b*x)
|
43,748 |
{9 \choose 3}*{6 \choose 3}*{3 \choose 1} = \frac{9!}{3!*3!*1!*2!} = 7! = 5040
|
7,940 |
\binom{m}{j} = \binom{m}{m - j} = (-1)^{m - j} \cdot \binom{-j + (-1)}{m - j}
|
16,376 |
d^2 = (d + 2)^2 - (d + 7\cdot (-1))^2 = (d + 2 + d + 7\cdot (-1))\cdot \left(d + 2 - d + 7\right) = 9\cdot (2\cdot d + 5\cdot \left(-1\right)) = 18\cdot d + 45\cdot (-1)
|
18,441 |
m*(h + g) = mh + mg
|
31,624 |
\left(2 + y \cdot 4\right)^2 = (2 + 4 \cdot y) \cdot (y \cdot 4 + 2)
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-26,664 |
\left(-5*q + 2*p\right)*(2*p + q*5) = 4*p * p - q^2*25
|
-12,691 |
4 = \dfrac{20}{5}
|
-17,723 |
8 = 16\cdot (-1) + 24
|
-30,277 |
\frac{1}{(-1) + x}*(4*(-1) + x^2 + 6*x) = x + 7 + \frac{3}{(-1) + x}
|
31,480 |
(a - b)^2 = (a - b)*(a - b) = \left(a - b\right)*a - (a - b)*b = a^2 - b*a - a*b + b^2
|
-23,356 |
\frac172\cdot 2/3 = \dfrac{4}{21}
|
-1,871 |
23/12 \pi - \pi*4/3 = \dfrac{1}{12}7 \pi
|
-1,760 |
4/3 \cdot \pi + \frac{\pi}{6} = \pi \cdot 3/2
|
22,560 |
12 = -(-144 + 228)*5 + 3*144
|
15,558 |
2(d - b) = b * b * b - d^2 * d = (b - d) \left(b^2 + db + d^2\right)
|
-3,705 |
m^5/m = \frac{m}{m}\cdot m\cdot m\cdot m\cdot m = m^4
|
15,154 |
\frac{1}{10^{\frac{1}{2}}} \cdot 3 = \cos(x)\Longrightarrow \frac{1}{10^{\frac{1}{2}}} = \sin(x)
|
-19 |
-5 + 3*(-1) = -8
|
10,808 |
(n + z) * (n + z) = n^2 + 2*n*z + z^2
|
30,640 |
a^2 \cdot a^2 \cdot a = a^5
|
27,367 |
\left(\sqrt{d} \sqrt{b}\right)^2 = \left(\sqrt{b d}\right)^2
|
19,631 |
m \cdot r_1 + m \cdot r_2 = (r_1 + r_2) \cdot m
|
46,290 |
0 + B = B = B + 0
|
10,686 |
\frac{\mathrm{d}}{\mathrm{d}y} \csc^2{y\times 4} = \frac{\mathrm{d}}{\mathrm{d}y} \csc^2{4\times y}
|
35,002 |
0 = k^2 - H^2\Longrightarrow H^2 = k \cdot k
|
-29,564 |
y^2*2 = \frac{y^3*2}{y}*1
|
14,360 |
|d_1 - d_2| + |d_2 - c| = -(d_1 - d_2) + d_2 - c = -d_1 + 2 \cdot d_2 - c
|
31,200 |
\cos\left(2\cdot x\right) = \cos^2(x)\cdot 2 + (-1)
|
-26,163 |
6\cdot 6 + 20\cdot (-1) - \frac{1}{4}\cdot 32 = 36 + 20\cdot \left(-1\right) + 8\cdot \left(-1\right) = 8
|
10,668 |
-\dfrac{y^6}{27 \cdot x^9} = \frac{(-1) \cdot y^6}{27 \cdot x^9} = \frac{y^6}{(-27) \cdot x^9}
|
8,677 |
(x + \beta)^2 - \beta*x*4 = (x - \beta) * (x - \beta)
|
19,522 |
\cos{5\times x} = \sin(\dfrac{5}{2}\times \pi - 5\times x) = \sin{5\times (\pi/2 - x)}
|
-1,379 |
\frac{7 \cdot 1/2}{(-1) \cdot 9 \cdot \frac17} = \frac72 \cdot \left(-\dfrac{1}{9} \cdot 7\right)
|
-4,954 |
\frac{1}{10} \cdot 2.7 = 2.7/10
|
946 |
1 + x + x^2 + \ldots + x^{\left(-1\right) + k} = \frac{x^k + \left(-1\right)}{(-1) + x}
|
18,963 |
5^n > 4^n = 2^{2*n} \gt 2^{n + 1} + 1
|
12,948 |
\left(2\cdot T^{\dfrac{1}{2}} = T \Rightarrow T^2 = 4\cdot T\right) \Rightarrow T^2 - T\cdot 4 = 0
|
19,241 |
1 + 2 + 3 + ... ... + 8 = \frac1272 = 36
|
-6,303 |
\frac{1}{3 \cdot (t + 9)} = \frac{1}{3 \cdot t + 27}
|
36,853 |
\dfrac{1}{32} + \frac{3}{32} = 1/8
|
30,106 |
(1 - \frac{1}{2^2}) \cdot (\tfrac{1}{2^2} + 1) = -\frac{1}{2^4} + 1
|
545 |
-(3*(-1) + \pi^2/3) + 1 = 4 - \tfrac{\pi^2}{3}
|
-27,759 |
d/dz \left(2\cdot \tan{z}\right) = 2\cdot \frac{d}{dz} \tan{z} = 2\cdot \sec^2{z}
|
22,414 |
((-1) + q) \cdot (q + 2 \cdot (-1))! = ((-1) + q)!
|
-22,317 |
\left(3 + H\right) \left(H + 8(-1)\right) = H^2 - H\cdot 5 + 24 \left(-1\right)
|
26,669 |
|(x + \frac{1}{2}) (x + \frac{1}{2}) + 7/4|/(\sqrt{2}) = \frac{1}{\sqrt{1 1 + 1^2}} |x + x^2 + 2|
|
13,180 |
\frac{a}{h} = (4 m + 1)^{\frac{1}{2}}\Longrightarrow \frac{a^2}{h^2} = 2 + 4 m
|
5,220 |
( 2(a + 5), 3(a + 5), 17) = ( 10 + 2a, 3a + 15, 17)
|
-22,719 |
\frac{40}{56} = 5*8/(7*8)
|
18,145 |
6 \cdot (-1) + 2^{l + 1} \cdot (3 + l^2 - l \cdot 2) = 6 \cdot \left(-1\right) + 2^{l + 1} \cdot (l \cdot (l + 2 \cdot (-1)) + 3)
|
23,016 |
-(-5^{1/2} \times d + x) = d \times 5^{1/2} - x
|
40,677 |
50388 = \binom{19}{7}
|
23,397 |
z = \sin\left(y\right) \Rightarrow z \cdot z = \sin^2\left(y\right)
|
18,878 |
\frac{1}{21} 5 = \dfrac{1}{\binom{7}{2}} (\binom{2}{2} + \binom{2}{2} + \binom{3}{2})
|
-5,929 |
\dfrac{3k}{k^2 - 36} = \dfrac{3k}{(k - 6)(k + 6)}
|
24,974 |
(\left(-1\right) + X) \cdot (1 + X) = \left(-1\right) + X^2
|
47,123 |
\frac{1 - \tan{\tfrac{x}{2}}}{1 + \tan{\frac{1}{2}*x}} = \tfrac{1}{1 + \tan{\frac{\pi}{4}}*\tan{\frac{x}{2}}}*(\tan{\pi/4} - \tan{\frac{x}{2}}) = \tan(\frac{\pi}{4} - x/2)
|
13,890 |
(x+1)^2 - (x+1) + 1 = x^2 +x +1
|
3,280 |
2\sqrt{3} + 4 = 3 + 2\sqrt{3} + 1
|
7,619 |
4 + y^2 - y = 6 + y^2 - y + 2*\left(-1\right)
|
-11,217 |
(Y + 2(-1))^2 + g = (Y + 2\left(-1\right)) \left(Y + 2(-1)\right) + g = Y^2 - 4Y + 4 + g
|
7,976 |
(V - E[V])^2 = E[V] \cdot E[V] + V^2 - E[V] \cdot V \cdot 2
|
11,895 |
(A + B)^2 = B^2 + A^2 + A\cdot B\cdot 2
|
22,001 |
\sin(B) = B - B^2 \cdot B/3! + B^5/5! - \ldots
|
-4,019 |
\dfrac{1}{q \cdot q}\cdot q^3\cdot \frac{10}{60} = \frac{q^3\cdot 10}{60\cdot q^2}
|
-10,500 |
-\dfrac{8}{2 \cdot x} \cdot \frac{1}{2} \cdot 2 = -\frac{16}{4 \cdot x}
|
850 |
2017 = \dfrac{1}{\sqrt{8 + 8} + 8 + 8}\cdot 8! + 8/8
|
19,411 |
10^4 + \left(-1\right) + 10^4 + \left(-1\right) = 2 \cdot 10^4 + 2 \cdot (-1) = 19998 \lt 10^5 + (-1)
|
-30,072 |
\frac{\mathrm{d}}{\mathrm{d}y} y^6 = 6y^5
|
-6,446 |
\frac{4 \times r}{8 \times (-1) + r^2 - r \times 7} \times 1 = \frac{4 \times r}{(8 \times \left(-1\right) + r) \times \left(1 + r\right)} \times 1
|
3,756 |
1 + \cdots + 1 = r = r = \frac{r}{t} + \cdots \cdot r/t = t \cdot \frac{r}{t}
|
25,412 |
h\cdot \dfrac{d}{d}\cdot d = h\cdot d
|
-18,628 |
-9 = 3\cdot \left(4\cdot x + 8\right) = 12\cdot x + 24 = 12\cdot x + 24
|
-26,171 |
\dfrac{1}{3}*21 + (-1) - \frac12*12 = 7 + (-1) + 6*\left(-1\right) = 0
|
-22,631 |
\frac18\cdot 5\cdot (-\frac18) = \frac{5}{8\cdot 8}\cdot (-1) = -\frac{5}{64} = -\frac{5}{64}
|
19,991 |
\frac{6}{2\cdot 2}\cdot 1 = \frac12\cdot 3 = 1.5
|
17,051 |
z_x - 2 \cdot x = \frac{1}{z_x + 2 \cdot x} \cdot (z_x \cdot z_x - 4 \cdot x^2) = \frac{1}{z_x + 2 \cdot x}
|
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