Use division to write the rational function in the form q(x) + r(x)/d(x), where the degree of r(x) is less than the degree of
d(x). Then find the partial fraction decomposition of r(x)/d(x).
-$\frac { 5 x ^ { 2 } - x - 10 } { x ^ { 2 } - 4 }$
A) $5 + \frac { 2 } { x - 2 } - \frac { 3 } { x + 2 }$
B) $\frac { 2 } { x - 2 } - \frac { 3 } { x + 2 }$
C) $5 + \frac { 3 } { x - 2 } - \frac { 2 } { x + 2 }$
D) $5 + \frac { 2 } { x - 2 } + \frac { 3 } { x - 2 }$

Question

Quizplus · Accepted Answer

First, divide $5x^2 - x - 10$ by $x^2 - 4$ to get $5 + \frac{9x - 10}{x^2 - 4}$. Then, factor the denominator and decompose $\frac{9x - 10}{x^2 - 4}$ into partial fractions to get $\frac{2}{x - 2} - \frac{3}{x + 2}$. Thus, the complete expression is $5 + \frac{2}{x - 2} - \frac{3}{x + 2}$.

Use Division to Write the Rational Function in the Form 5x2−x−10x2−4\frac { 5 x ^ { 2 } - x - 10 } { x ^ { 2 } - 4 }x2−45x2−x−10​

Use Division to Write the Rational Function in the Form $\frac { 5 x ^ { 2 } - x - 10 } { x ^ { 2 } - 4 }$