Evaluate
-\frac{x^{3}+3x^{2}+x+51}{\left(x+3\right)\left(x^{2}-25\right)}
Expand
-\frac{x^{3}+3x^{2}+x+51}{\left(x+3\right)\left(x^{2}-25\right)}
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\frac{x+3}{\left(x-5\right)\left(x+5\right)}-\frac{x-1}{x-5}+\frac{3}{x+3}
Factor x^{2}-25.
\frac{x+3}{\left(x-5\right)\left(x+5\right)}-\frac{\left(x-1\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}+\frac{3}{x+3}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and x-5 is \left(x-5\right)\left(x+5\right). Multiply \frac{x-1}{x-5} times \frac{x+5}{x+5}.
\frac{x+3-\left(x-1\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}+\frac{3}{x+3}
Since \frac{x+3}{\left(x-5\right)\left(x+5\right)} and \frac{\left(x-1\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+3-x^{2}-5x+x+5}{\left(x-5\right)\left(x+5\right)}+\frac{3}{x+3}
Do the multiplications in x+3-\left(x-1\right)\left(x+5\right).
\frac{-3x+8-x^{2}}{\left(x-5\right)\left(x+5\right)}+\frac{3}{x+3}
Combine like terms in x+3-x^{2}-5x+x+5.
\frac{\left(-3x+8-x^{2}\right)\left(x+3\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}+\frac{3\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and x+3 is \left(x-5\right)\left(x+3\right)\left(x+5\right). Multiply \frac{-3x+8-x^{2}}{\left(x-5\right)\left(x+5\right)} times \frac{x+3}{x+3}. Multiply \frac{3}{x+3} times \frac{\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}.
\frac{\left(-3x+8-x^{2}\right)\left(x+3\right)+3\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}
Since \frac{\left(-3x+8-x^{2}\right)\left(x+3\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)} and \frac{3\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.
\frac{-3x^{2}-9x+8x+24-x^{3}-3x^{2}+3x^{2}+15x-15x-75}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}
Do the multiplications in \left(-3x+8-x^{2}\right)\left(x+3\right)+3\left(x-5\right)\left(x+5\right).
\frac{-3x^{2}-x-51-x^{3}}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}
Combine like terms in -3x^{2}-9x+8x+24-x^{3}-3x^{2}+3x^{2}+15x-15x-75.
\frac{-3x^{2}-x-51-x^{3}}{x^{3}+3x^{2}-25x-75}
Expand \left(x-5\right)\left(x+3\right)\left(x+5\right).
\frac{x+3}{\left(x-5\right)\left(x+5\right)}-\frac{x-1}{x-5}+\frac{3}{x+3}
Factor x^{2}-25.
\frac{x+3}{\left(x-5\right)\left(x+5\right)}-\frac{\left(x-1\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}+\frac{3}{x+3}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and x-5 is \left(x-5\right)\left(x+5\right). Multiply \frac{x-1}{x-5} times \frac{x+5}{x+5}.
\frac{x+3-\left(x-1\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}+\frac{3}{x+3}
Since \frac{x+3}{\left(x-5\right)\left(x+5\right)} and \frac{\left(x-1\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{x+3-x^{2}-5x+x+5}{\left(x-5\right)\left(x+5\right)}+\frac{3}{x+3}
Do the multiplications in x+3-\left(x-1\right)\left(x+5\right).
\frac{-3x+8-x^{2}}{\left(x-5\right)\left(x+5\right)}+\frac{3}{x+3}
Combine like terms in x+3-x^{2}-5x+x+5.
\frac{\left(-3x+8-x^{2}\right)\left(x+3\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}+\frac{3\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and x+3 is \left(x-5\right)\left(x+3\right)\left(x+5\right). Multiply \frac{-3x+8-x^{2}}{\left(x-5\right)\left(x+5\right)} times \frac{x+3}{x+3}. Multiply \frac{3}{x+3} times \frac{\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}.
\frac{\left(-3x+8-x^{2}\right)\left(x+3\right)+3\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}
Since \frac{\left(-3x+8-x^{2}\right)\left(x+3\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)} and \frac{3\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\left(x+3\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.
\frac{-3x^{2}-9x+8x+24-x^{3}-3x^{2}+3x^{2}+15x-15x-75}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}
Do the multiplications in \left(-3x+8-x^{2}\right)\left(x+3\right)+3\left(x-5\right)\left(x+5\right).
\frac{-3x^{2}-x-51-x^{3}}{\left(x-5\right)\left(x+3\right)\left(x+5\right)}
Combine like terms in -3x^{2}-9x+8x+24-x^{3}-3x^{2}+3x^{2}+15x-15x-75.
\frac{-3x^{2}-x-51-x^{3}}{x^{3}+3x^{2}-25x-75}
Expand \left(x-5\right)\left(x+3\right)\left(x+5\right).
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