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-4,302 | \frac{p*36}{72*p^3} = \frac{p}{p^3}*\frac{1}{72}*36 |
16,580 | \frac{y}{15}\cdot 2 = y\cdot 2/15 |
4,719 | a^3 - d^3 = \left(d^2 + a^2 + d \cdot a\right) \cdot \left(a - d\right) |
8,689 | 1 + z^{\frac13} = 0 rightarrow z^{\tfrac{1}{3}} = -1 |
23,985 | 5^7\cdot 2 + 2\cdot 5^5 + 2\cdot 5^6 = 193750 |
3,535 | 0 \cdot \binom{n}{0} + \binom{n}{1} + 6 \cdot \binom{n}{2} + 6 \cdot \binom{n}{3} = n^3 |
42,368 | \int \dfrac{\cot(u)}{\sin(u)}\,du = \int \csc(u) \cdot \cot(u)\,du = -\csc(u) |
-427 | (e^{\frac16 \cdot π \cdot i \cdot 5})^9 = e^{\frac16 \cdot 5 \cdot i \cdot π \cdot 9} |
-22,266 | \left(1 + a\right) \cdot (a + 8 \cdot (-1)) = 8 \cdot (-1) + a^2 - 7 \cdot a |
15,680 | \sin^p(\|z\|)/\|z\| = \|z\|^{p + \left(-1\right)} \cdot \frac{1}{\|z\|^p} \cdot \sin^p(\|z\|) |
4,855 | (x + 1)^2 \cdot \left(x + 1\right) = x^3 + 3 \cdot x^2 + 3 \cdot x + 1 < x \cdot x \cdot x + x^3 + x^3 |
4,114 | ((B + C)^2 - B \cdot C \cdot 2)^2 - 2 \cdot B^2 \cdot C^2 = B^4 + C^4 |
46,519 | \left(a_n = \sqrt{a_{n + \left(-1\right)} \cdot a_{1 + n}}\Longrightarrow a_n^2 = a_{n + 1} \cdot a_{n + (-1)}\right)\Longrightarrow \frac{a_n}{a_{n + (-1)}} = a_{1 + n}/(a_n) |
-7,995 | \tfrac{(-20 \cdot i - 30) \cdot (1 - 5 \cdot i)}{(1 - i \cdot 5) \cdot \left(5 \cdot i + 1\right)} = \frac{1}{-(i \cdot 5)^2 + 1^2} \cdot (-20 \cdot i - 30) \cdot (-5 \cdot i + 1) |
-10,401 | \dfrac{3}{h^2\cdot 20}\cdot 2/2 = \frac{6}{h^2\cdot 40} |
17,846 | (x^2)^{1/2} = ((-x) \cdot (-x))^{1/2} = |x| |
34,364 | 0 > 1 + x rightarrow x \lt -1 |
21,509 | -\frac12*\pi = ((-1)*\pi)/2 |
21,960 | \tfrac12(3(-1) + 3^{m + (-1)}) + 1 = (3^{m + (-1)} + (-1))/2 |
5,883 | r*(x_1 + x_2) = r*x_1 + r*x_2 |
37,797 | z_1 + z_2 = z_2 - z_1 + 2\cdot z_1 |
35,849 | (n^2 + n + 1) \cdot (n^3 - n + 1) = 1 + n^5 + n^4 |
39,265 | \cos{i\cdot y} = (e^{-y} + e^y)/2 = \cosh{y} |
-22,905 | \frac{8*5}{5*5} = 40/25 |
17,886 | 1/(f_1 f_2) = \frac{1}{f_2 f_1} |
-4,278 | \frac{a^4}{a^3} \cdot 44/132 = \frac{a^4 \cdot 44}{a^3 \cdot 132} |
-18,372 | \dfrac{7 + y^2 + 8 \cdot y}{y^2 + y \cdot 7} = \dfrac{1}{y \cdot (y + 7)} \cdot (y + 1) \cdot (y + 7) |
23,330 | \binom{x}{m} = \frac{1}{m! (x - m)!} x! |
20,602 | e^{\frac43 \times \pi \times i} = (e^{\pi \times i \times 2/3})^2 |
-4,693 | \dfrac{1}{y^2 + y\cdot 2 + 15\cdot (-1)}\cdot (y\cdot 2 + 2) = \frac{1}{3\cdot (-1) + y} + \dfrac{1}{5 + y} |
-9,185 | 72 z + 16 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 z + 2 \cdot 2 \cdot 2 \cdot 2 |
34,435 | 8881 = 9025 + 144\times \left(-1\right) |
4,818 | x - d + a - b = a + x - b + d |
11,919 | \left(\left(z/2 = z\cdot 2 + 2(-1)\Longrightarrow z = z\cdot 4 + 4(-1)\right)\Longrightarrow 3z = 4\right)\Longrightarrow \frac43 = z |
10,158 | (x^2 + y^2) * (x^2 + y^2) = x^4 + x * x*y^2 + y^4 + x * x*y^2 = x^2 + x^2*y^2 |
-6,142 | \tfrac{4}{z \cdot z + z\cdot 13 + 36} = \frac{1}{(9 + z) \left(z + 4\right)}4 |
-10,433 | -\frac{1}{s\cdot 4}\cdot \left(s\cdot 4 + \left(-1\right)\right)\cdot 20/20 = -\frac{1}{80\cdot s}\cdot (80\cdot s + 20\cdot (-1)) |
17,271 | 0 = q^{j + (-1)}*b*b = q^{j + (-1)}*b^2 = q^{j + 2*\left(-1\right)}*b*q*b |
14,437 | \sum_{i=1}^x b_i + c\sum_{i=1}^x a_i = \sum_{i=1}^x (a_i c + b_i) |
18,564 | \dfrac{1}{7}\cdot 4 = 1 - \dfrac27 - 1/7 |
-20,541 | 6/6 \cdot (-10 \cdot t + 4)/(-8) = \left(-60 \cdot t + 24\right)/(-48) |
32,094 | 2^0 \times 747 = 747 |
5,788 | 1995*d + 1995^2 = 1995*(1995 + d) |
10,547 | z^3-z^{-3}=(z-z^{-1})(z^2+1+z^{-2}) |
8,623 | (y + 2(-1)) (y + 4) = y^2 + 2y + 8(-1) |
-23,224 | 1 - 2/3 = \frac{1}{3} |
5,923 | \tfrac{2}{1 + x^2} \cdot x^2 = 2 - \frac{2}{x^2 + 1} |
24,688 | 2 = |z| = |z + 4 (-1) + 4| \leq |z + 4 (-1)| + 4 |
4,767 | 4 \cdot (-1) + x = 1 \Rightarrow x = 5 |
24,602 | (\dfrac12)^2 + (\frac{1}{2}) * (\frac{1}{2}) = 1/2 |
25,383 | ( A \times Y, B \times Y) = (B \times Y)^T \times A \times Y = Y^T \times B^T \times A \times Y = Y^T \times B^T \times A \times Y |
-16,012 | 5/10 = -7 \cdot \frac{5}{10} + 8 \cdot \tfrac{5}{10} |
5,966 | (1 - z)\cdot \left(1 + z + z^2\right) = -z^3 + 1 |
31,549 | z^3 + z^2 - z*10 + 8 = (z + 4)*(z + 2*(-1))*(z + (-1)) |
-3,485 | \dfrac{1}{100}\cdot 4 = 0.04 |
3,348 | 3 + \frac19 = 3.111 \cdot \dotsm \approx \pi |
-20,096 | \frac{7}{a\cdot 7 + 42\cdot (-1)} = \frac{7\cdot 1/7}{a + 6\cdot (-1)} |
16,432 | d_2 \cdot d_2 + d_1^2 = 0 \Rightarrow d_1^2 = -d_2^2 |
29,749 | Y' \cdot T + X' \cdot Y' + X \cdot T = X \cdot Y' \cdot T + X' \cdot Y' \cdot T + X' \cdot Y' + X \cdot T = X' \cdot Y' + X \cdot T |
-26,425 | \dfrac{1}{z^k}z^l = z^{-k + l} |
29,154 | i^2 = i^6 = i^{10}\cdot \dotsm\cdot i^{38} |
23,070 | 9^k + 4^{k + 1} = \left(5 + 4\right)^k + 4^{k + 1} = 5\cdot b + 4^k + 4^{k + 1} = 5\cdot b + 5\cdot 4^k |
-5,488 | \frac{2 \cdot t}{(t + (-1)) \cdot (4 \cdot (-1) + t)} \cdot 1 = \frac{2 \cdot t}{t^2 - 5 \cdot t + 4} |
1,531 | 0.35^3\cdot 0.65 = 0.35^3\cdot 0.65\cdot (0.35 + 0.65)^7 |
-8,015 | (-4 - i\cdot 4)/(-2) = -\frac{1}{-2}\cdot 4 - 4\cdot i/(-2) |
-4,411 | \frac{5 + 3 \cdot z}{12 \cdot (-1) + z \cdot z + z} = \dfrac{2}{z + 3 \cdot (-1)} + \frac{1}{z + 4} |
-25,276 | 4/3 \times 27^{\frac{1}{3}} = 4/3 \times 3 = 4 |
-19,036 | \frac{7}{15} = \frac{D_s}{9 \cdot π} \cdot 9 \cdot π = D_s |
5,203 | \frac{1}{3!\cdot 2!\cdot 1!}\cdot 6! = \frac42\cdot 6\cdot 5 = 60 |
-13,001 | 26 + 11 (-1) = 15 |
-4,266 | \frac15\times k\times 2 = 2/5\times k |
7,978 | 4/10*5/11 = \frac{1}{11} 2 |
45,626 | \cos^2{z} = \cos^2{z} |
30,592 | (x + (-1))^2 + 4\cdot x = (x + 1)^2 |
43,914 | 2 = 6 - (10 - 6) |
4,639 | (\sqrt{13} + 3)/16 = (1 + \left((-1) + \sqrt{13}\right)/4)/4 |
9,340 | \left((\frac{1}{2^{1 / 2}}) \cdot (\frac{1}{2^{1 / 2}}) + (\frac{1}{2^{\frac{1}{2}}})^2\right)^{\frac{1}{2}} = (1/2 + \frac{1}{2})^{1 / 2} = 1 |
126 | \sin{\theta}/(2*\sin{\frac{1}{2}*\theta}) = \cos{\frac{\theta}{2}} |
-562 | e^{\frac{i*\pi}{3}*1*3} = (e^{\frac{i}{3}*\pi})^3 |
-2,736 | \sqrt{6}\cdot 4 + \sqrt{6} = \sqrt{6} + \sqrt{16} \sqrt{6} |
19,106 | ( E*B*e, d) = ( B*e, E*d) = ( e, B*E*d) |
27,266 | q*q*x = q^2*x |
6,517 | \left\{C,B\right\}\Longrightarrow B = \{\overline{C},\overline{B}\} |
38,092 | z \in A \Rightarrow z \in A |
11,334 | \frac{\text{d}}{\text{d}x} \tan{x} = \sec^2{x} = 1 + \tan^2{x} |
1,095 | 2 \times a - a + 1 = 2 \times a - a + (-1) = a + (-1) |
8,741 | 9000 - 9^4 = 9000 + 6561\times (-1) = 2439 |
16,849 | \int \frac{1}{1 + y^2} \cdot (1 + y^4 + \left(-1\right))\,\mathrm{d}y = \int \dfrac{y^4}{y \cdot y + 1}\,\mathrm{d}y |
-6,392 | \dfrac{1}{(j + 6)\times (j + 9)}\times j = \frac{1}{54 + j^2 + 15\times j}\times j |
-10,782 | -15 = 5 \cdot m + 30 + 6 = 5 \cdot m + 36 |
-8,065 | \frac{45 \cdot i + 5}{5 - 5 \cdot i} \cdot \frac{5 + i \cdot 5}{5 \cdot i + 5} = \frac{5 + 45 \cdot i}{5 - 5 \cdot i} |
10,279 | (u + w)*(-w + u) = u * u - w^2 |
1,711 | \dfrac{5}{5 + 4}\cdot \frac{6}{6 + 3} = 30/81 \approx 0.37 |
11,513 | \frac{\mathrm{d}}{\mathrm{d}x} \tan^{-1}(x) = \dfrac{1}{\sec^2(\tan^{-1}(x))} |
29,730 | u \cdot ( \dfrac{1}{2}, \dfrac12) = 0 = u \cdot \left( 1/2, \tfrac{1}{2}\right) |
-5,393 | \frac{1}{10^6}\cdot 28.0 = \dfrac{28}{10^6} |
272 | 9! - 2! \cdot 8! \cdot 3 + 3 \cdot 2! \cdot 7! = 151200 |
-4,416 | (z + 5) \left(z + (-1)\right) = z^2 + 4z + 5(-1) |
6,143 | g \cdot g \cdot g - c^3 = (-c + g) \cdot (g^2 + g \cdot c + c^2) |
-2,328 | 10/18 - 4/18 = 6/18 |
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