Find the partial fraction decomposition for the rational expression.
-$$\frac { 26 x ^ { 2 } - 88 x + 76 } { ( x - 2 ) ( 2 x - 3 ) ^ { 2 } }$$
A) $\frac { 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { - 4 } { x - 2 }$
B) $\frac { - 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { 4 } { x - 2 }$
C) $\frac { 5 } { 2 x - 3 } + \frac { - 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 4 } { x - 2 }$
D) $\frac { - 4 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { 5 } { x - 2 }$

Question

Quizplus · Accepted Answer

The correct partial fraction decomposition for the given rational expression is achieved by breaking it down into simpler fractions that can be combined to form the original expression. The denominator suggests a decomposition involving terms of $(x - 2)$, $(2x - 3)$, and $(2x - 3)^2$. Option C correctly represents this decomposition, aligning with the structure of the denominator and the coefficients determined through partial fraction decomposition techniques.

Find the Partial Fraction Decomposition for the Rational Expression 26x2−88x+76(x−2)(2x−3)2\frac { 26 x ^ { 2 } - 88 x + 76 } { ( x - 2 ) ( 2 x - 3 ) ^ { 2 } }(x−2)(2x−3)226x2−88x+76​

Find the Partial Fraction Decomposition for the Rational Expression $\frac { 26 x ^ { 2 } - 88 x + 76 } { ( x - 2 ) ( 2 x - 3 ) ^ { 2 } }$