Evaluate
\frac{x^{3}-8x^{2}+16x-100}{7\left(x^{2}+9\right)}
Expand
\frac{x^{3}-8x^{2}+16x-100}{7\left(x^{2}+9\right)}
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\frac{7\left(x-4\right)}{7\left(x^{2}+9\right)}-\frac{\left(8-x\right)\left(x^{2}+9\right)}{7\left(x^{2}+9\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2}+9 and 7 is 7\left(x^{2}+9\right). Multiply \frac{x-4}{x^{2}+9} times \frac{7}{7}. Multiply \frac{8-x}{7} times \frac{x^{2}+9}{x^{2}+9}.
\frac{7\left(x-4\right)-\left(8-x\right)\left(x^{2}+9\right)}{7\left(x^{2}+9\right)}
Since \frac{7\left(x-4\right)}{7\left(x^{2}+9\right)} and \frac{\left(8-x\right)\left(x^{2}+9\right)}{7\left(x^{2}+9\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{7x-28-8x^{2}-72+x^{3}+9x}{7\left(x^{2}+9\right)}
Do the multiplications in 7\left(x-4\right)-\left(8-x\right)\left(x^{2}+9\right).
\frac{16x-100-8x^{2}+x^{3}}{7\left(x^{2}+9\right)}
Combine like terms in 7x-28-8x^{2}-72+x^{3}+9x.
\frac{16x-100-8x^{2}+x^{3}}{7x^{2}+63}
Expand 7\left(x^{2}+9\right).
\frac{7\left(x-4\right)}{7\left(x^{2}+9\right)}-\frac{\left(8-x\right)\left(x^{2}+9\right)}{7\left(x^{2}+9\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x^{2}+9 and 7 is 7\left(x^{2}+9\right). Multiply \frac{x-4}{x^{2}+9} times \frac{7}{7}. Multiply \frac{8-x}{7} times \frac{x^{2}+9}{x^{2}+9}.
\frac{7\left(x-4\right)-\left(8-x\right)\left(x^{2}+9\right)}{7\left(x^{2}+9\right)}
Since \frac{7\left(x-4\right)}{7\left(x^{2}+9\right)} and \frac{\left(8-x\right)\left(x^{2}+9\right)}{7\left(x^{2}+9\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{7x-28-8x^{2}-72+x^{3}+9x}{7\left(x^{2}+9\right)}
Do the multiplications in 7\left(x-4\right)-\left(8-x\right)\left(x^{2}+9\right).
\frac{16x-100-8x^{2}+x^{3}}{7\left(x^{2}+9\right)}
Combine like terms in 7x-28-8x^{2}-72+x^{3}+9x.
\frac{16x-100-8x^{2}+x^{3}}{7x^{2}+63}
Expand 7\left(x^{2}+9\right).
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