Evaluate
\frac{57+13x+3x^{2}-x^{3}}{4\left(x-1\right)\left(x+5\right)}
Expand
-\frac{x^{3}-3x^{2}-13x-57}{4\left(x-1\right)\left(x+5\right)}
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\frac{\left(x+2\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)}+\frac{\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x+5\right)}-\frac{x+1}{4}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x+5 is \left(x-1\right)\left(x+5\right). Multiply \frac{x+2}{x-1} times \frac{x+5}{x+5}. Multiply \frac{x-3}{x+5} times \frac{x-1}{x-1}.
\frac{\left(x+2\right)\left(x+5\right)+\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x+5\right)}-\frac{x+1}{4}
Since \frac{\left(x+2\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)} and \frac{\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+5x+2x+10+x^{2}-x-3x+3}{\left(x-1\right)\left(x+5\right)}-\frac{x+1}{4}
Do the multiplications in \left(x+2\right)\left(x+5\right)+\left(x-3\right)\left(x-1\right).
\frac{2x^{2}+3x+13}{\left(x-1\right)\left(x+5\right)}-\frac{x+1}{4}
Combine like terms in x^{2}+5x+2x+10+x^{2}-x-3x+3.
\frac{4\left(2x^{2}+3x+13\right)}{4\left(x-1\right)\left(x+5\right)}-\frac{\left(x+1\right)\left(x-1\right)\left(x+5\right)}{4\left(x-1\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+5\right) and 4 is 4\left(x-1\right)\left(x+5\right). Multiply \frac{2x^{2}+3x+13}{\left(x-1\right)\left(x+5\right)} times \frac{4}{4}. Multiply \frac{x+1}{4} times \frac{\left(x-1\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)}.
\frac{4\left(2x^{2}+3x+13\right)-\left(x+1\right)\left(x-1\right)\left(x+5\right)}{4\left(x-1\right)\left(x+5\right)}
Since \frac{4\left(2x^{2}+3x+13\right)}{4\left(x-1\right)\left(x+5\right)} and \frac{\left(x+1\right)\left(x-1\right)\left(x+5\right)}{4\left(x-1\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{8x^{2}+12x+52-x^{3}-4x^{2}+5x-x^{2}-4x+5}{4\left(x-1\right)\left(x+5\right)}
Do the multiplications in 4\left(2x^{2}+3x+13\right)-\left(x+1\right)\left(x-1\right)\left(x+5\right).
\frac{3x^{2}+13x+57-x^{3}}{4\left(x-1\right)\left(x+5\right)}
Combine like terms in 8x^{2}+12x+52-x^{3}-4x^{2}+5x-x^{2}-4x+5.
\frac{3x^{2}+13x+57-x^{3}}{4x^{2}+16x-20}
Expand 4\left(x-1\right)\left(x+5\right).
\frac{\left(x+2\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)}+\frac{\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x+5\right)}-\frac{x+1}{4}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and x+5 is \left(x-1\right)\left(x+5\right). Multiply \frac{x+2}{x-1} times \frac{x+5}{x+5}. Multiply \frac{x-3}{x+5} times \frac{x-1}{x-1}.
\frac{\left(x+2\right)\left(x+5\right)+\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x+5\right)}-\frac{x+1}{4}
Since \frac{\left(x+2\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)} and \frac{\left(x-3\right)\left(x-1\right)}{\left(x-1\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.
\frac{x^{2}+5x+2x+10+x^{2}-x-3x+3}{\left(x-1\right)\left(x+5\right)}-\frac{x+1}{4}
Do the multiplications in \left(x+2\right)\left(x+5\right)+\left(x-3\right)\left(x-1\right).
\frac{2x^{2}+3x+13}{\left(x-1\right)\left(x+5\right)}-\frac{x+1}{4}
Combine like terms in x^{2}+5x+2x+10+x^{2}-x-3x+3.
\frac{4\left(2x^{2}+3x+13\right)}{4\left(x-1\right)\left(x+5\right)}-\frac{\left(x+1\right)\left(x-1\right)\left(x+5\right)}{4\left(x-1\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+5\right) and 4 is 4\left(x-1\right)\left(x+5\right). Multiply \frac{2x^{2}+3x+13}{\left(x-1\right)\left(x+5\right)} times \frac{4}{4}. Multiply \frac{x+1}{4} times \frac{\left(x-1\right)\left(x+5\right)}{\left(x-1\right)\left(x+5\right)}.
\frac{4\left(2x^{2}+3x+13\right)-\left(x+1\right)\left(x-1\right)\left(x+5\right)}{4\left(x-1\right)\left(x+5\right)}
Since \frac{4\left(2x^{2}+3x+13\right)}{4\left(x-1\right)\left(x+5\right)} and \frac{\left(x+1\right)\left(x-1\right)\left(x+5\right)}{4\left(x-1\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{8x^{2}+12x+52-x^{3}-4x^{2}+5x-x^{2}-4x+5}{4\left(x-1\right)\left(x+5\right)}
Do the multiplications in 4\left(2x^{2}+3x+13\right)-\left(x+1\right)\left(x-1\right)\left(x+5\right).
\frac{3x^{2}+13x+57-x^{3}}{4\left(x-1\right)\left(x+5\right)}
Combine like terms in 8x^{2}+12x+52-x^{3}-4x^{2}+5x-x^{2}-4x+5.
\frac{3x^{2}+13x+57-x^{3}}{4x^{2}+16x-20}
Expand 4\left(x-1\right)\left(x+5\right).
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