Question

step-by-Step how do i solve
(x^2 + 12)/(x^2 – 2x - 35)

Answer 1

Are you trying to simplify or solve for the variable x?

Answer 2

If you're trying to simplify, I couldn't boil it down to something simpler than\[\frac{x^2+12}{x^2-2x-35}=\frac{x^2+12}{(x-7)(x+5)}\]\[\frac{x^2+12}{(x-7)(x+5)}=\frac{A}{x-7}+\frac{B}{x+5}\]\[A(x+5)+B(x-7)=x^2+12\]\[-12B=37\implies B=-\frac{37}{12}\]\[12A=61\implies A=\frac{61}{12}\]\[\frac{x^2+12}{(x-7)(x+5)}=\frac{61}{12}\frac{1}{x-7}+-\frac{37}{12}\frac{1}{x+5}\]

Answer 3

does that work since we have an improper fraction

Answer 4

\[\frac{x^2-2x-35}{x^2-2x-35}+\frac{2x+47}{x^2-2x-35}=1+\frac{2x+47}{x^2-2x-35}\]

Answer 5

\[\frac{2x+47}{x^2-2x-35}=\frac{2x+47}{(x-7)(x+5)}=\frac{A}{x-7}+\frac{B}{x+5}\]
\[=\frac{A(x+5)+B(x-7)}{(x-7)(x+5)}=\frac{x(A+B)+5A-7B}{(x-7)(x+5)}\]

Answer 6

\[=>2x+47=(A+B)x+(5A-7B)\]

Answer 7

\[A+B=2 ; 5A-7B=47\]

Answer 8

A+B=2 5A-7B=47
7(A+B=2)
7A+7B=14
+(7A+7B=14)
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12A+0=61
12A=61
A=61/12
Remember A+B=2
which implies B=2-A
B=2-61/12=(24-61)/12
B=-37/12

Answer 9

\[\frac{x^2-2x-35}{x^2-2x-35}+\frac{2x+47}{x^2-2x-35}=1+\frac{2x+47}{x^2-2x-35} \]
\[=1+\frac{61}{12} \cdot \frac{1}{x-7}+\frac{-37}{12} \cdot \frac{1}{x+5}\]