id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
20,080 |
e^u \cdot e^v = e^{u + v}
|
31,474 |
x^2 - z*x*5 + z^2*6 = (-z*2 + x)*(x - 3*z)
|
4,481 |
x\cdot (x + 3)^{1/2} = -(x + 3)^{1/2}\cdot 3 + \left(x + 3\right)^{3/2}
|
14,501 |
z^{f + b} = z^f \cdot z^b
|
-23,701 |
\tfrac{5}{56} = 5\cdot 1/8/7
|
-10,441 |
-\dfrac{1}{p*3 + 9*(-1)}*10*\dfrac{2}{2} = -\frac{20}{p*6 + 18*(-1)}
|
8,327 |
\left(e^{4 - 4 \cdot A} = e \implies 1 = 4 - 4 \cdot A\right) \implies A = 3/4
|
19,166 |
(4\cdot g_1)^2 - 4\cdot 10\cdot g_2 = 16\cdot g_1^2 - 40\cdot g_2 = 8\cdot \left(2\cdot g_1^2 - 5\cdot g_2\right)
|
11,083 |
\frac{1}{x^{n!}}\cdot x^{(n + 1)!} = x^{\left(n + 1\right)! - n!} = x^{n!\cdot (n + 1 + (-1))} = x^{n\cdot n!}
|
7,001 |
11 + 24/(c*3) + 12 (-1) = c*12 \implies (-1) + \frac{8}{c} = c*12
|
392 |
-\dfrac{11}{16} + \dfrac{5}{16}\cdot 3 = 1/4
|
23,507 |
(12 m + n)^2 = n^2 + 144 m^2 + 24 n m
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34,540 |
c*(d + a)*x = x*c*(d + a)
|
-20,662 |
-\dfrac{10}{7} \cdot \frac{p + 5}{5 + p} = \frac{1}{35 + 7 \cdot p} \cdot \left(50 \cdot (-1) - 10 \cdot p\right)
|
13,522 |
x\cdot z = 0 \Rightarrow x = 0\text{ or }z = 0
|
10,700 |
139 + x^2 + x \cdot 26 = (x + 13)^2 + 30 (-1)
|
16,794 |
5 = 120 + 25 \left(-1\right) + 34 \left(-1\right) + 26 (-1) + 10 (-1) + 20 (-1)
|
16,301 |
\left(10^4 - 10^2\right) \times 0.0012121212 \times \dots = 9900 \times 12/9900 = 12
|
1,517 |
\beta \cdot B \cdot x + x \cdot A \cdot \alpha = (A \cdot \alpha + B \cdot \beta) \cdot x
|
22,163 |
3 + 6\cdot y = 0 \Rightarrow -1/2 = y
|
-20,917 |
\dfrac{8 + x*6}{8 + x*6}*8/3 = \dfrac{48*x + 64}{18*x + 24}
|
-7,699 |
\dfrac{1}{4 - 3*i}*(10 - 20*i)*\frac{3*i + 4}{4 + i*3} = \dfrac{1}{4 - 3*i}*\left(-20*i + 10\right)
|
-1,265 |
\frac{15}{72} = \frac{5}{72*1/3}*1 = 5/24
|
-24,658 |
\tfrac{2}{2*9}*1 = 2/18
|
4,801 |
t^4 + 1 = (t^2 + (-1))^2 + 2 \cdot t^2 = (t^2 + (-1))^2 - t \cdot t = (t^2 - t + (-1)) \cdot (t^2 + t + (-1))
|
24,212 |
z = 2^{\frac13} + \sqrt{2} \Rightarrow (z - \sqrt{2})^3 = 2
|
-22,273 |
(x + 1) \cdot (10 + x) = x^2 + 11 \cdot x + 10
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-20,369 |
\frac55 \times \frac{1}{6 + t \times 9} \times \left(-2 \times t + 3 \times \left(-1\right)\right) = \frac{1}{t \times 45 + 30} \times (15 \times (-1) - t \times 10)
|
9,093 |
(-1)\cdot (-1) + 3 + 4\cdot (-1) = 0
|
-17,505 |
78 + 75 (-1) = 3
|
751 |
\binom{2^n}{2} + \left(-1\right) = (2^n + 1)\cdot \left(2^{\left(-1\right) + n} + (-1)\right)
|
20,237 |
\dfrac14 = 1 + 2\left(-1\right) + 3 + 4\left(-1\right) + 5 + 6\left(-1\right) + 7 + 8(-1) + 9 + 10 \left(-1\right) + \dots
|
-19,783 |
0.8 = \frac{1}{25}*20
|
13,478 |
2 \cdot (z^2 + x \cdot x + x \cdot z) = (z + x)^2 + x \cdot x + z^2
|
-4,392 |
\frac{3}{l} \cdot 1/11 = \tfrac{3}{11 \cdot l}
|
16,278 |
(1 + z)^{i + 1} = (1 + z) (1 + z)^i \geq (1 + z) \left(1 + iz\right)
|
39,493 |
-10 = 11 \cdot (-1) + 1
|
11,068 |
15 = \frac12\cdot (60\cdot (-1) + 90)
|
-6,170 |
\tfrac{x}{(x + 4)*(x + 1)} = \dfrac{x}{x^2 + 5*x + 4}
|
18,874 |
7\cdot 0.3 = \dfrac{1}{10} 3\cdot 7
|
11,162 |
c_3 + 4 + 3 = 13 \Rightarrow 6 = c_3
|
13,677 |
0 = \frac{1}{x^2*2 + 7*x + 5}*(x*4 + 13)\Longrightarrow 0 = 4*x + 13
|
36,322 |
-11 + 19 \times \left(-1\right) = -30
|
-20,528 |
\frac99\cdot \tfrac{p}{8 + p}\cdot 10 = \frac{90\cdot p}{p\cdot 9 + 72}
|
11,504 |
30 + 450 + 300 + 180 + 150 \cdot (-1) + 60 \cdot \left(-1\right) + 90 \cdot (-1) = 660
|
-6,017 |
\dfrac{1}{15 + 5 r} 4 = \frac{1}{5 (r + 3)} 4
|
48,714 |
26 = 2 + 3\cdot 8
|
-6,597 |
\frac{1}{6 + 2s} = \frac{1}{2(s + 3)}
|
-1,364 |
\frac{1/2*9}{\frac{1}{5} (-2)} = -5/2*9/2
|
1,301 |
(A - B)^2 = B^2 + A^2 - 2AB
|
13,510 |
19 - (16*(-1) + 19)*6 = \left(-5\right)*19 + 6*16
|
28,768 |
Lx + dg = dg + Lx
|
14,280 |
\dfrac{1}{2} + \epsilon = (1 - 1/2 + \epsilon)
|
-9,403 |
-2*2*2*3*3 + 2*2*2*5*x = 72*(-1) + 40*x
|
27,533 |
q \cdot x \cdot i \cdot r = 2 \cdot x \cdot i \cdot q \cdot \frac{1}{2} \cdot r
|
-718 |
π\frac{19}{12} = -14 π + 187/12 π
|
12,066 |
-(-1)*x + n = x + n
|
22,130 |
\binom{19}{2} \binom{1}{1}/(\binom{20}{3}) = \dfrac{1}{20}3
|
5,312 |
\dfrac{\frac{47}{60}}{3}1 = 47/180 \approx \frac{1}{3.8}
|
-2,277 |
-\frac{3}{14} + 6/14 = \frac{1}{14}3
|
12,093 |
x^2 - 3\cdot x = x^2 - 3\cdot x + (\tfrac{3}{2})^2 - (3/2) \cdot (3/2) = (x - \dfrac12\cdot 3)^2 - (3/2)^2
|
14,487 |
\frac{1}{(t + (-1)) \cdot (t + (-1))} = -\frac{\mathrm{d}}{\mathrm{d}t} \frac{1}{t + (-1)}
|
-7,077 |
\frac{6}{91} = 3/13*4/14
|
17,093 |
\left(72 \gt c \implies c = 66\right) \implies 78 = -c + 144
|
14,898 |
\frac23 \cdot \dfrac175 = \frac132 \cdot 15/21
|
-6,260 |
\frac{4}{\left(a + 2 \cdot \left(-1\right)\right) \cdot 2} = \frac{4}{a \cdot 2 + 4 \cdot (-1)}
|
25,931 |
54912 = \binom{13}{1}\cdot \binom{4}{3}\cdot \binom{4}{1}^2\cdot \binom{12}{2}
|
28,288 |
\frac{h^2}{h \cdot h} \cdot g^{12} = g^{27} = \frac{1}{h^3} \cdot g^8 \cdot h^2 \cdot h = \frac1g \cdot g^9
|
-1,871 |
\frac{23}{12}*\pi - \frac{4}{3}*\pi = 7/12*\pi
|
10,525 |
-\pi/6 + 2*\pi = 11*\pi/6
|
-4,433 |
\frac{5 - y}{y^2 + y\times 8 + 15} = \frac{4}{3 + y} - \frac{1}{y + 5}\times 5
|
19,719 |
x/x = x \cdot y_1 \cdot \dots \cdot y_k = x \cdot y_1 \cdot \dots \cdot x \cdot y_k
|
19,180 |
-|\sin\left(x\right)| + x \gt -|\sin(x)| \Rightarrow 0 < x
|
25,847 |
5 \cdot \frac{1}{3} \cdot 5^3 = 625/3
|
39,252 |
\sin^2(\theta) = 1 - \cos^2(\theta)
|
24,227 |
(1 + x)\times (x^8 + x^6 + x^4 + x^2 + 1)\times (x + (-1)) = (-1) + x^{10}
|
-9,911 |
-0.25 = -\tfrac18 \cdot 2
|
3,230 |
\int f\,\mathrm{d}\mu = \int f\cdot |\mu|\cdot d\cdot \frac{1}{d\cdot |\mu|}\,\mathrm{d}\mu
|
15,477 |
4 \times (n + 1) \times (n + (-1)) + 8 \times (n + 1) - n + 1 = 4 \times (n + 1) \times (n + (-1) + 2) - n + 1 = 4 \times (n + 1)^2 - n + 1
|
-6,214 |
\frac{2}{t*3 + 24} = \dfrac{1}{3*(8 + t)}*2
|
9,346 |
\operatorname{Var}(-C + X) = \operatorname{Var}(X + C)
|
-1,113 |
-35/35 = (\left(-35\right)\cdot \frac{1}{35})/(35\cdot \frac{1}{35}) = -1
|
5,166 |
\left(-1\right)^{\dfrac32} = -(-1)^{\frac12} = -i
|
38,092 |
y \in D \Rightarrow y \in D
|
14,099 |
-\left(-1\right) e_2 + e_1 = e_1 + e_2
|
-20,632 |
\dfrac{1}{72 p}\left(p \cdot (-27)\right) = \frac{p}{p \cdot 9}9 (-3/8)
|
16,583 |
0 = \Im{(2\pi)}
|
7,585 |
x_1\cdot x_2 = 0 = x_1\cdot x_2
|
23,836 |
40 + 34*(-1) = 6
|
16,882 |
\tfrac{5}{\sqrt{100}} = 0.5
|
4,734 |
\frac21\cdot 1/\left(-4\right) \tfrac21 = 4/(-4) = -1
|
-5,410 |
6.7/10 = 6.7\cdot 10^{-1}/1000 = \frac{1}{10000}\cdot 6.7
|
29,966 |
1140 = \frac{1}{3! \cdot 17!} \cdot 20!
|
41,955 |
7 + 2 \times 15 = 37
|
4,913 |
s = r^{a \cdot m} \cdot s^{b \cdot m} = \left(r^a \cdot s^b\right)^m
|
-4,024 |
\frac{10}{3}p = \dfrac{10}{3} p
|
1,727 |
-(\left(-6\right)^3*4 + 27 (-2) * (-2)) = 756
|
-19,025 |
\dfrac{1}{5} = \frac{C_x}{9 \pi}\cdot 9 \pi = C_x
|
-9,325 |
-2\cdot 2\cdot 2\cdot 2\cdot 2 - 2\cdot 2\cdot 3\cdot 3\cdot k = 32\cdot (-1) - k\cdot 36
|
-11,631 |
-9 + i*19 = -4 + 5*\left(-1\right) + i*19
|
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