Evaluate
\frac{-x^{4}-14x^{3}+x^{2}+7x-10}{x^{2}-4}
Expand
\frac{-x^{4}-14x^{3}+x^{2}+7x-10}{x^{2}-4}
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\frac{\left(3x^{3}+5\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{\left(4x^{3}-x\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+2 and x-2 is \left(x-2\right)\left(x+2\right). Multiply \frac{3x^{3}+5}{x+2} times \frac{x-2}{x-2}. Multiply \frac{4x^{3}-x}{x-2} times \frac{x+2}{x+2}.
\frac{\left(3x^{3}+5\right)\left(x-2\right)-\left(4x^{3}-x\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}
Since \frac{\left(3x^{3}+5\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} and \frac{\left(4x^{3}-x\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{4}-6x^{3}+5x-10-4x^{4}-8x^{3}+x^{2}+2x}{\left(x-2\right)\left(x+2\right)}
Do the multiplications in \left(3x^{3}+5\right)\left(x-2\right)-\left(4x^{3}-x\right)\left(x+2\right).
\frac{-x^{4}-14x^{3}+7x-10+x^{2}}{\left(x-2\right)\left(x+2\right)}
Combine like terms in 3x^{4}-6x^{3}+5x-10-4x^{4}-8x^{3}+x^{2}+2x.
\frac{-x^{4}-14x^{3}+7x-10+x^{2}}{x^{2}-4}
Expand \left(x-2\right)\left(x+2\right).
\frac{\left(3x^{3}+5\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{\left(4x^{3}-x\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+2 and x-2 is \left(x-2\right)\left(x+2\right). Multiply \frac{3x^{3}+5}{x+2} times \frac{x-2}{x-2}. Multiply \frac{4x^{3}-x}{x-2} times \frac{x+2}{x+2}.
\frac{\left(3x^{3}+5\right)\left(x-2\right)-\left(4x^{3}-x\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}
Since \frac{\left(3x^{3}+5\right)\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} and \frac{\left(4x^{3}-x\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{4}-6x^{3}+5x-10-4x^{4}-8x^{3}+x^{2}+2x}{\left(x-2\right)\left(x+2\right)}
Do the multiplications in \left(3x^{3}+5\right)\left(x-2\right)-\left(4x^{3}-x\right)\left(x+2\right).
\frac{-x^{4}-14x^{3}+7x-10+x^{2}}{\left(x-2\right)\left(x+2\right)}
Combine like terms in 3x^{4}-6x^{3}+5x-10-4x^{4}-8x^{3}+x^{2}+2x.
\frac{-x^{4}-14x^{3}+7x-10+x^{2}}{x^{2}-4}
Expand \left(x-2\right)\left(x+2\right).
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