id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
7,318 |
\frac{1}{2} \cdot (3 + 5^{1/2}) = \frac{3}{2} + 5^{1/2}/2
|
27,367 |
\left(\sqrt{a}\cdot \sqrt{b}\right)^2 = (\sqrt{a\cdot b})^2
|
50,517 |
10010 = 2 \cdot 5 \cdot 7 \cdot 11 \cdot 13
|
13,136 |
-j^2 + (1 + j)^2 = 1 + j \cdot 2
|
-4,841 |
\dfrac{79.2}{10^7} = \frac{1}{10^7} \cdot 79.2
|
19,207 |
\frac{\partial}{\partial x} (w \cdot x) = w \cdot \frac{dx}{dx} + x \cdot \frac{dw}{dx}
|
1,433 |
\dfrac{6}{8} \cdot \dfrac{1}{10 \cdot 9} \cdot \dfrac57 \cdot 24 \cdot 3 = 3/7
|
2,272 |
x > -s + s_n \Rightarrow s + x > s_n
|
9,131 |
(p^x + 3) \cdot (p^x + \left(-1\right)) + 4 = p^{2 \cdot x} + 2 \cdot p^x + 1 = (p^x + 1)^2
|
-6,344 |
\frac{2}{(x + 8) (6 + x)} \frac{2}{2} = \frac{1}{2(8 + x) (x + 6)}4
|
3,372 |
(n + 1)*2 + (-1) = 1 + 2*n
|
23,869 |
x^4 + 4 = x^4 + 4\cdot x^2 + 4 - 4\cdot x^2 = (x \cdot x + 2)^2 - \left(2\cdot x\right)^2 = (x^2 - 2\cdot x + 2)\cdot (x \cdot x + 2\cdot x + 2)
|
-23,044 |
-1/2 (-\frac14) = 1/8
|
1,448 |
m = \frac{3}{2} \cdot y\Longrightarrow y = 2/3 \cdot m
|
30,745 |
\frac{1}{(1 + 1)*(1 + 2)*4}*(3 + 1) = 1/(3*1*2)
|
6,010 |
y/3\cdot 3 = y
|
21,222 |
-e^{32} + 384*\left(-1\right) = -384 - e^{32}
|
-10,301 |
-24 = -x + 2 \cdot \left(-1\right) + 4 = -x + 2
|
1,047 |
\dfrac{30}{7} = \frac{(4 + 1)\cdot 6}{1 + 6}
|
21,940 |
36 = (6\cdot (-1) + 30 + 12\cdot (-1))\cdot 3
|
3,787 |
1/y = \frac{1}{y \times \overline{y}} \times \overline{y}
|
23,608 |
\left(17 + 3 \cdot \sqrt{34}\right) \cdot \left(17 - 3 \cdot \sqrt{34}\right) = -17
|
16,483 |
60 = (25 - 6 d) (25 - 4 d) - (25 - 7 d) (25 - 2 d) = 25 - 10 d
|
32,210 |
1 + {n + 1 \choose n} = {n + 2 \choose n + 1}
|
12,294 |
(g + d)/2 = (2\cdot g + d - g)/2 = g + \dfrac{1}{2}\cdot \left(d - g\right)
|
-20,991 |
7/7 \cdot \frac{1}{-3} \cdot (8 \cdot x + 7 \cdot (-1)) = \dfrac{1}{-21} \cdot (56 \cdot x + 49 \cdot (-1))
|
-507 |
e^{14*3 \pi i/4} = (e^{\frac{1}{4} \pi i*3})^{14}
|
15,294 |
\frac{x}{\sqrt{x \cdot x + h}\cdot 2}\cdot 2 = \frac{1}{\sqrt{x^2 + h}}\cdot x
|
4,652 |
\frac{1}{\sqrt{f} + \sqrt{a}} \cdot (f - a) = -\sqrt{a} + \sqrt{f}
|
2,031 |
-60*348*t + t*20915 = 35*t
|
-20,537 |
-9/(-9)*(-1/7) = 9/(-63)
|
31,022 |
(x + 1)^2 - x^2 = x*2 + 1
|
11,569 |
a \cdot b = \frac{1}{1/a \cdot 1/b} = \frac{1}{1/b \cdot 1/a} = b \cdot a
|
22,682 |
c + g + x = x + c + g
|
28,789 |
\lim_{h \to 0} \left(y^2 + 2yh + h^2 - y^2\right)/h = \lim_{h \to 0} \frac{1}{h}\left(h^2 + 2hy\right)
|
6,111 |
(1 + 2/k)^k = (\frac1k\cdot (k + 2))^k = \left(\frac{k + 2}{k + 1}\right)^k\cdot ((k + 1)/k)^k
|
25,238 |
\cot(\frac{\pi}{4} - z) = \tan(z + \frac{\pi}{4})
|
6,043 |
-(1 + a'^2 + 3a') + a^2 + 3a + 1 = (a - a') (3 + a + a')
|
4,785 |
(-2)^2 - 4y^2 = 4(1-y^2)
|
-2,203 |
-1/11 + 4/11 = \frac{3}{11}
|
-4,565 |
\left(3 + z\right)*(z + 2) = 6 + z^2 + 5*z
|
-22,343 |
(1 + r) \cdot (r + 6) = 6 + r^2 + 7 \cdot r
|
25,305 |
\mathbb{P}(x) = \mathbb{P}(x)\cdot \cos{x} \implies \cos{x} = 1
|
26,190 |
0 + 0 + 3\cdot \frac{1}{3}\cdot t = t
|
29,521 |
4 \cdot a = (a + 1 + x)^2 = a^2 + 2 \cdot (1 + x) \cdot a + (1 + x) \cdot (1 + x)
|
13,690 |
\frac{1}{c_1 c_2} = 1/(c_1 c_2)
|
6,021 |
x^{1/c} = x^{\dfrac1c}
|
22,547 |
36 X - N = 35 X - N - X
|
15,574 |
(h + b)^2 = b^2 + h^2 + 2 b h
|
13,342 |
C_2*C_1^l = C_2*C_1^l
|
-4,571 |
\dfrac{5 + w}{w^2 - w \cdot 8 + 15} = -\dfrac{4}{w + 3 \cdot (-1)} + \frac{5}{5 \cdot (-1) + w}
|
36,225 |
72 = 9(-1) + 9^2
|
24,746 |
f + e + x = f + e + x
|
-20,942 |
\frac16 6 (-\dfrac{1}{t + 9 (-1)} 2) = -\frac{12}{54 \left(-1\right) + 6 t}
|
-5,862 |
\dfrac{1}{10 + 5 \cdot t} \cdot 3 = \frac{1}{5 \cdot (2 + t)} \cdot 3
|
-21,905 |
-1/6 - \frac{7}{4} = -1*2/(6*2) - 7*3/(4*3) = -\frac{1}{12}2 - 21/12 = -(2 + 21 (-1))/12 = -23/12
|
4,750 |
\dfrac12 \cdot (1 + 5^{1/2}) = \dfrac12 + 5^{1/2}/2
|
4,665 |
\sin2A+\sin2B+2\sin(A+B)=\cdots=4\sin(A+B)\cdot\sin^2\dfrac{A-B}2
|
5,504 |
\frac{4 + \tfrac3x}{-5/x + 7} = \dfrac{1}{7x + 5(-1)}(4x + 3)
|
43,627 |
\frac{1}{2}\cdot 3 = \frac{3}{2}
|
7,001 |
12\cdot b = 11 + \frac{1}{3\cdot b}\cdot 24 + 12\cdot (-1) \implies 12\cdot b = (-1) + 8/b
|
-22,229 |
18 + l^2 + l \cdot 11 = \left(l + 9\right) \cdot (l + 2)
|
-5,889 |
\frac{1}{z*4 + 36 (-1)} 3 = \dfrac{1}{4 \left(z + 9 (-1)\right)} 3
|
-20,772 |
\frac{24 - 8\cdot m}{m\cdot 5 + 15\cdot (-1)} = \frac{1}{m + 3\cdot (-1)}\cdot (3\cdot (-1) + m)\cdot (-8/5)
|
49,130 |
1 - 99/100\cdot 98/99\cdot 97/98\cdot 96/97\cdot \frac{95}{96} = 1 - 0.95 = 0.05 = \frac{1}{20}
|
-16,920 |
-2 = -2(-5z) - 16 = 10 z - 16 = 10 z + 16 (-1)
|
36,974 |
x^0 e^{xq} = e^{qx}
|
18,638 |
\dfrac{1}{b \times h} = \frac{1}{h \times b}
|
-5,412 |
2.56\cdot 10 = \frac{25.6}{10^6}\cdot 1 = \frac{2.56}{10^5}
|
-10,278 |
\frac55\cdot \frac{7 + 4\cdot x}{6 + 3\cdot x} = \frac{1}{15\cdot x + 30}\cdot (20\cdot x + 35)
|
21,221 |
1/3 + \frac13 = \dfrac{2}{3}
|
205 |
-(e\cdot i\cdot z/2 - e^{\left((-1)\cdot i\cdot z\right)/2})^2 = -\left(2\cdot i\right)^2\cdot \sin^2\left(z/2\right) = 4\cdot \sin^2(z/2)
|
16,239 |
24 + 9\left(-1\right) = 15
|
6,206 |
-1/((-1)\cdot \frac{1}{3}) = 3
|
-18,924 |
\dfrac{7}{12} = \dfrac{1}{36 \cdot \pi} \cdot E_s \cdot 36 \cdot \pi = E_s
|
11,925 |
\frac{1}{\sqrt{\frac{1}{n} (n + \left(-1\right))} \sqrt{\frac1n ((-1) + n)}} (1/n*\left(-1\right)) = -\frac{1}{n + (-1)}
|
14,495 |
1 - r^3 = 1 + r + r^2 - r^3 + r + r^2
|
24,966 |
u = e^z + 2 \Rightarrow \frac{\text{d}u}{\text{d}z} = e^z = u + 2 \cdot (-1)
|
20,754 |
2\cdot (-1) + x^2 = \left(x + \sqrt{2}\right)\cdot (x - \sqrt{2})
|
7,366 |
\mathbb{E}[x\cdot I] = \sqrt{\mathbb{E}[x^2]\cdot \mathbb{E}[I^2]}
|
19,355 |
\left(w + x + y + z\right)^2 = 2*(w*z + x*y + x*z + w*x + z*y + y*w) + x^2 + y^2 + z^2 + w^2
|
-21,573 |
\cos\left(-\pi \frac{1}{3}2\right) = -0.5
|
23,190 |
(y + (-1))^2 = 1 + y \cdot y - 2y
|
18,007 |
π \cdot (-\frac{8}{3} + 4 \cdot (-1) + 16) = π \cdot 28/3
|
40,195 |
180 \cdot 2 = 360
|
-24,505 |
1 + 32/8 = 1 + 4 = 5
|
4,428 |
3/4*5/4 = \tfrac{1}{16}*15 = 0.9375
|
-15,808 |
\frac{1}{10} \cdot 7 - 5 \cdot 9/10 = -38/10
|
-10,634 |
6/6*\frac{2*t + 1}{15*t + 20} = \frac{t*12 + 6}{120 + t*90}
|
15,462 |
H + 2 = \frac{1}{H + 2*(-1)}*(H + 2)*(H + 2*\left(-1\right)) = \frac{1}{H + 2*(-1)}*\left(H^2 + 4*\left(-1\right)\right)
|
49,888 |
74 = 4 + 7\times 10 = 9 + 5\times 13
|
6,763 |
-x*(-\varepsilon) = x*\varepsilon
|
-7,023 |
1/8 = \frac18*3*\frac{3}{9}
|
11,435 |
a^2 + d^2 - 2\cdot a\cdot d = (a - d) \cdot (a - d)
|
24,756 |
(1 - t^2)^{-k} (1 - t)^{-k} = (1 - t)^{-k} (1 + t)^{-k} (1 - t)^{-k} = (1 - t)^{-2k} (1 + t)^{-k}
|
-10,277 |
30 = 10\cdot t + 16 + 50\cdot \left(-1\right) = 10\cdot t + 34\cdot \left(-1\right)
|
13,130 |
\|A + x\|^2 = qp\cdot (A + x)^W\cdot (A + x) = qp\cdot \left(A^W + x^W\right) (A + x) = qp\cdot (A^W A + A^W x + x^W A + x^W x)
|
-1,120 |
-\frac128 = ((-8) \frac{1}{2})/\left(2\cdot \frac{1}{2}\right) = -4
|
23,627 |
\frac12\cdot (-(k + (-1)) + N)\cdot \left(-((-1) + k) + N + 1\right) = (N - k + 2)\cdot \left(N - k + 1\right)/2
|
12,437 |
(-1)^{\frac{1}{n}} = (e^{\pi\cdot i})^{1/n} = e^{\frac{\pi\cdot i}{n}\cdot 1}
|
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