Question

Which expression represents the correct form for the quotient and remainder, written as partial fractions, of StartFraction 7 x squared minus 40 x + 52 Over x squared minus 6 x + 9 EndFraction?

Answer 1

Answer:

$A + \frac{B}{x-3} + \frac{C}{(x-3)^{2} }$

Step-by-step explanation:

First, because the degree of the numerator is the same as the degree of the denominator, this fraction needs simplified further by long division. Upon simplification, the rational expression is $7+\frac{2x-11}{x^2-6x+9}$.

Next, the denominatior needs factored in order to split up the second part of the simplified expression into two different partial fractions. Such factorization yields us, $(x-3)^{2}$.

Finally, we have all of our necessary information to set up all of our partial fractions.

This gives us $A + \frac{B}{x-3} + \frac{C}{(x-3)^{2} }$, which is our answer.