Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$
A) $\frac { 7 } { x - 1 } + \frac { 1 } { ( x + 1 ) ^ { 3 } }$
B) $\frac { 7 } { x - 1 } - \frac { 1 } { ( x + 1 ) ^ { 2 } }$
C) $\frac { 7 } { ( x - 1 ) ^ { 2 } } - \frac { 1 } { ( x - 1 ) ^ { 3 } }$
D) $\frac { 7 } { x - 1 } - \frac { 1 } { ( x - 1 ) ^ { 2 } }$
E) $\frac { 7 } { x - 1 } + \frac { 1 } { ( x - 1 ) ^ { 2 } }$

Question

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$ ​
A) $\frac { 7 } { x - 1 } + \frac { 1 } { ( x + 1 ) ^ { 3 } }$
B) $\frac { 7 } { x - 1 } - \frac { 1 } { ( x + 1 ) ^ { 2 } }$
C) $\frac { 7 } { ( x - 1 ) ^ { 2 } } - \frac { 1 } { ( x - 1 ) ^ { 3 } }$
D) $\frac { 7 } { x - 1 } - \frac { 1 } { ( x - 1 ) ^ { 2 } }$
E) $\frac { 7 } { x - 1 } + \frac { 1 } { ( x - 1 ) ^ { 2 } }$

Quizplus · Accepted Answer

The denominator can be factored as $(x-1)^2$. So, the partial fraction decomposition is of the form $\frac{A}{x-1}+\frac{B}{(x-1)^2}$. Multiplying both sides by $(x-1)^2$, we get $7x-8=A(x-1)+B$. Substituting $x=1$, we get $-8=-A$, so $A=8$. Substituting $x=0$, we get $-8=B$, so $B=-8$. Therefore, the partial fraction decomposition is $\frac{8}{x-1}-\frac{8}{(x-1)^2}$.

Write the Partial Fraction Decomposition of the Rational Expression 7x−8(x−1)2\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }(x−1)27x−8​

Write the Partial Fraction Decomposition of the Rational Expression $\frac { 7 x - 8 } { ( x - 1 ) ^ { 2 } }$