Find the partial fraction decomposition.
-$\frac { 6 } { 4 x ^ { 2 } - 36 }$
A) $\frac { 1 / 2 } { 2 x - 6 } + \frac { - 1 / 2 } { ( 2 x - 6 ) ^ { 2 } }$
B) $\frac { 1 } { 2 x - 6 } + \frac { - 1 } { 2 x + 6 }$
C) $\frac { 1 / 2 } { 2 x + 6 } + \frac { - 1 / 2 } { 2 x - 6 }$
D) $\frac { 1 / 2 } { 2 x - 6 } + \frac { - 1 / 2 } { 2 x + 6 }$

Question

Quizplus · Accepted Answer

The denominator $4x^2 - 36$ can be factored as $(2x)^2 - 6^2 = (2x - 6)(2x + 6)$. The partial fraction decomposition splits the fraction into two parts, each with one of these factors in the denominator. The coefficients $1/2$ and $-1/2$ are determined by solving the equation for the numerators to match the original fraction.

Find the Partial Fraction Decomposition 64x2−36\frac { 6 } { 4 x ^ { 2 } - 36 }4x2−366​

Find the Partial Fraction Decomposition $\frac { 6 } { 4 x ^ { 2 } - 36 }$