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14,278 | \binom{1 + m}{x} = \binom{m}{x} + \binom{m}{x + (-1)} |
-20,324 | -\frac12*3*\frac{4*(-1) + x}{4*(-1) + x} = \tfrac{1}{8*(-1) + 2*x}*(12 - 3*x) |
21,614 | 1 + 25 w^2 - 10 w = (5 w + (-1))^2 |
15,082 | \frac{1}{e^{bx} + 1} = \frac{e^{-xb}}{e^{-xb} + 1} |
-9,144 | z \cdot z \cdot 2 \cdot 2 \cdot 5 = z^2 \cdot 20 |
21,147 | (k + 1)^{k + 1} = (1 + k)^k \cdot \left(k + 1\right) |
25,538 | 2 \cdot (x^2 - 3 \cdot x + 1) + x \cdot 7 + (-1) = 1 + x^2 \cdot 2 + x |
-3,044 | 4^{1/2}\cdot 7^{1/2} + 9^{1/2}\cdot 7^{1/2} = 3\cdot 7^{1/2} + 7^{1/2}\cdot 2 |
19,615 | 12 = {4 \choose 3} \cdot 3 |
6,288 | \cos(2 \cdot x/2) = \cos(x) |
-12,895 | 8 + 8 + 7 = 23 |
-7,956 | \frac{1}{-i - 2}\cdot (-2 - i)\cdot \dfrac{1}{i - 2}\cdot (8 + i) = \dfrac{1}{i - 2}\cdot (8 + i) |
-1,450 | -5/45 = \left((-5)*\frac15\right)/(45*\frac{1}{5}) = -1/9 |
26,135 | (c + d)^2 - (-g^2 + d \cdot c) \cdot 4 = g \cdot g \cdot 4 + (d - c)^2 |
4,863 | \sin\left(b + a\right) = \sin{a} \cos{b} + \cos{a} \sin{b} |
28,533 | \cos\left(2*D\right) = 2*\cos^2(D) + (-1) |
21,959 | 52 \frac{(-1) + 98^4}{(-1) + 98} = 9944*9945/2 |
13,274 | \frac{1}{2^2} = \frac{1}{2^2}\cdot 2^0 = \dfrac14 |
26,022 | \int 1/\left(\sqrt{z}\right)\,\mathrm{d}z = \int z^{-\dfrac12}\,\mathrm{d}z |
14,914 | (x + b)^{1 + n} = (b + x)*(b + x)^n |
16,921 | 10 \cdot x = \dfrac{1}{-2} \cdot \left(\left(-20\right) \cdot x\right) = -0.5 \cdot \left(-20 \cdot x\right) |
-23,348 | 3/4 \cdot \frac49 = \dfrac{1}{3} |
-15,150 | \frac{1}{(d^4 x^2)^5 x} = \frac{1}{d^{20} x^{10} x} |
11,293 | -35 \cdot (f + a \cdot y) - 2 \cdot a = -35 \cdot a \cdot y - a \cdot 2 + f \cdot 35 |
21,275 | \left(1 + l\right)! = \left(l + 1\right)*l*...*2 |
6,860 | \left(-1\right)^{\tfrac{1}{2}} + \frac{1}{1/2} = (-1)^{1/2} + 2 = 2 + i |
16,358 | 2^{7.16} = 2^{716/100} = \sqrt[100]{2^{716}} |
3,824 | \mathbb{E}(\bar{X})^2 + Var(\bar{X}^2) = \mathbb{E}(\bar{X}^2) |
-18,979 | \frac29 = \frac{1}{36 \cdot \pi} \cdot A_s \cdot 36 \cdot \pi = A_s |
-1,502 | -\frac92*\frac{9}{2} = ((-1)*9*\frac12)/\left(2*1/9\right) |
913 | \sin{C} \cdot \cos{C} \cdot 2 = \sin{2 \cdot C} |
-19,591 | \dfrac{1/6 \cdot 5}{1/7 \cdot 6} = 7/6 \cdot 5/6 |
18,380 | \left(b + a\right) \cdot (a + b) \cdot \left(b + a\right) = (b + a)^3 |
-4,200 | 27/54 \frac{x^4}{x^5} = \dfrac{x^4 \cdot 27}{x^5 \cdot 54} |
7,198 | \frac{\text{d}}{\text{d}x} \sin^2{3 x} = 2 \sin{3 x} \cos{3 x}*3 = 6 \sin{3 x} \cos{3 x} |
10,857 | \dfrac{1}{6^2}(6^2 - 1^2) = 1 - \frac{1}{36} |
-26,628 | 9m^2+30mn+25n^2=(3m+5n)^2 |
37,207 | 4! \times 3 \times 5! = 8640 |
13,073 | C*E = x_n \Rightarrow E*C = x_n |
11,423 | \tan(\arctan(y) + \arctan\left(y^3\right)) = \frac{1}{1 - y^4}\times (y + y \times y \times y) = \frac{y}{1 - y^2} |
43,751 | 416965528 = {140 \choose 5} |
165 | 4 + n*21 = \left(n*14 + 3\right) + n*7 + 1 |
10,305 | \left(g + b = b\cdot g \implies b\cdot g - g - b = 0\right) \implies (b + (-1))\cdot ((-1) + g) = 1 |
-5,734 | \dfrac{3}{10*(-1) + t*5} = \frac{3}{5*(2*(-1) + t)} |
-25,894 | 6.75 = 27/4 |
-20,206 | \frac77 \dfrac{7(-1) + f}{f + \left(-1\right)} = \frac{7f + 49 (-1)}{7f + 7(-1)} |
-15,678 | \frac{(\frac{1}{z^5})^2}{1/n\cdot \frac{1}{z \cdot z}} = \frac{1}{z^{10}\cdot \frac{1}{n\cdot z^2}} |
-13,232 | \frac{1}{-0.0009}*0.000243 = -0.27 |
9,811 | \dfrac{1}{4 \cdot 5} = -\frac15 + \dfrac{1}{4} |
5,104 | a + b\times \omega + c\times \omega^2 = a + b\times \omega - c\times \left(1 + \omega\right) = a - c + (b - c)\times \omega |
22,898 | -\tfrac{1}{2} = \dfrac{1}{-\sqrt{1} + (-1)} |
5,306 | q + 1 = 0\Longrightarrow q = -1 |
15,357 | 4ua = q^2 \Rightarrow q^2 = au*4 |
31,391 | \sin{z}\cdot \cos{z} = \sin{z}\cdot \sin(\frac{\pi}{2} - z) |
-19,013 | \dfrac12 = \frac{A_s}{16\cdot \pi}\cdot 16\cdot \pi = A_s |
-1,833 | \frac{7}{6} π = 2/3 π + \dfrac{π}{2} |
-11,495 | i*3 + 1 + 4 = 5 + 3*i |
21,582 | B \times B \times B + H^3 = \left(B^2 + H \times H - H\times B\right)\times (H + B) |
-23,356 | \frac{4}{21} = \frac{2}{7} \times \frac{2}{3} |
35,794 | \sin(x+\pi/2)=\cos x |
26,133 | 1/4 = \frac{1}{2}\cdot (1^{-1} - 1/2) |
14,931 | G = A \cdot T \Rightarrow \frac{\mathrm{d}G}{\mathrm{d}A} = A \cdot \frac{\mathrm{d}T}{\mathrm{d}A} + T |
-23,027 | \frac{10}{9 \cdot 10} \cdot 7 = \dfrac{70}{90} |
-28,818 | \left(2 + 6\right)/2 = 8/2 = 4 |
1,753 | \frac{1 - c^2}{1 - c} = c + 1 |
23,735 | -(3 k + 4) + 0 = 0 \implies k = -4/3 |
-5,540 | \dfrac{1}{(t + 2) \cdot 3} \cdot 5 = \frac{1}{6 + 3 \cdot t} \cdot 5 |
-22,839 | \dfrac{21}{28} = 3\cdot 7/(4\cdot 7) |
17,725 | (a + b)^n = a^n + a^{n + \left(-1\right)}\cdot b\cdot {n \choose 1} + ... |
31,533 | (3(-1) + 3^5)/5 = 48 |
11,875 | 9699 = 53 + \frac{1}{2}\cdot 19292 |
-11,499 | 2 i + 1 + 3 = 4 + i*2 |
11,470 | \frac{1}{z \cdot 2} \cdot (2 + z) = \dfrac{z}{z \cdot 2} + \frac{2}{2 \cdot z} |
17,415 | -(x^2 + z^2) + (z + x) * (z + x) = xz*2 |
24,680 | \mathbb{E}[x^2] = \mathbb{E}[x] \times \mathbb{E}[x] + \mathbb{Var}[x] |
-3,070 | 8 \cdot 3^{1/2} = 3^{1/2} \cdot \left(1 + 5 + 2\right) |
-4,407 | \left(x + 3 \cdot \left(-1\right)\right) \cdot (4 \cdot (-1) + x) = x^2 - x \cdot 7 + 12 |
6,081 | (x + \alpha\cdot y)^2 = x^2 + \alpha^2\cdot y^2 + x\cdot y\cdot \alpha\cdot 2 |
-430 | e^{11 \pi i \cdot 7/6} = (e^{7\pi i/6})^{11} |
26,456 | E\left(X \cdot Y\right) = E\left(X \cdot X \cdot X\right) = 0 = E\left(X\right) \cdot E\left(Y\right) |
-3,889 | \dfrac43*z^3 = \frac{4*z^3}{3} |
37,847 | z\cdot e = z\cdot e |
2,557 | \tfrac{32}{144} = \dfrac29 |
22,926 | G^c \cap (B \cap C) = G^c \cap \left(B \cap C\right) = C \cap (B \cap G^c) = C \cap (B \cap (G^c)) = \left(B \cap G^c\right) \cap (C \cap G^c) |
21,482 | \dfrac{(-2)^k}{3^{k + 1}} = \left(-2/3\right)^k/3 |
-20,775 | 8/8*\frac{1}{x + 5*(-1)}*(-6*x + 2) = \frac{-48*x + 16}{40*(-1) + x*8} |
-25,362 | d/dz \cot(z) = -\frac{1}{\sin^2\left(z\right)} |
-10,740 | \frac{2*k + 9*(-1)}{k + 3}*4/4 = \frac{8*k + 36*(-1)}{4*k + 12} |
17,522 | 2*3^2 + 3 \left(7/2\right) \left(7/2\right) = \frac{219}{4} \neq 17 |
35,153 | 247 + 127*(-1) = 120 |
17,747 | \frac{1}{D^T D} = \dfrac{1}{DD^T} |
31,429 | 1/C + \frac{1}{G} + 1/Z = (GZ + ZC + CG)/(CZ G) |
13,432 | x_1 + x_2 + \dots + x_{1 + n} = x_1 \cdot x_2 \cdot \dots \cdot x_{n + 1} |
-2,742 | 5^{\dfrac{1}{2}} \cdot \left(4 + 5 \cdot \left(-1\right) + 2\right) = 5^{1 / 2} |
-22,272 | 15\cdot (-1) + a^2 + a\cdot 2 = (a + 5)\cdot (3\cdot (-1) + a) |
39,596 | (f + (-1)) \cdot (f + (-1)) + \left(b + 1\right)^2 = f^2 + b \cdot b + 2\cdot (b + 1 - f) \leq f^2 + b^2 |
5,182 | \frac{\partial}{\partial x} \left(e \cdot x\right) = \frac{dx}{dx} \cdot e + x \cdot \frac{de}{dx} |
14,296 | 3 + b = a + 3 \Rightarrow b = a |
36,266 | 2 \cdot 2^{k + (-1)} = 2^1 \cdot 2^{k + \left(-1\right)} = 2^{1 + k + (-1)} = 2^k |
31,484 | y^b \cdot y^a = y^{b + a} |
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