Perform the indicated operation. Simplify if possible.
-$$\frac { 5 } { x + 2 } + \frac { 7 } { x ^ { 2 } + 4 x + 4 } - \frac { x } { x ^ { 2 } - 4 }$$
A) $\frac { 4 x ^ { 2 } + 5 x - 34 } { ( x + 2 ) ( x - 2 ) }$
B) $\frac { 6 x ^ { 2 } + 9 x - 34 } { ( x + 2 ) ^ { 2 } ( x - 2 ) }$
C) $\frac { 4 x ^ { 2 } + 5 x - 34 } { ( x + 2 ) ^ { 2 } ( x - 2 ) }$
D) $\frac { - x + 12 } { ( x + 2 ) ^ { 2 } ( x - 2 ) }$

Question

Quizplus · Accepted Answer

To simplify the given expression, first recognize that the denominators can be factored or are already in factored form:- The second term's denominator, $x^2 + 4x + 4$, is a perfect square and can be written as $(x + 2)^2$.- The third term's denominator, $x^2 - 4$, is a difference of squares and can be factored into $(x + 2)(x - 2)$.To add or subtract fractions, we need a common denominator, which in this case is $(x + 2)^2(x - 2)$.1. For the first term, multiply both numerator and denominator by $(x + 2)(x - 2)$ to get $\frac{5(x + 2)(x - 2)}{(x + 2)^2(x - 2)}$.2. The second term already has $(x + 2)^2$ in the denominator, so multiply the numerator and denominator by $(x - 2)$ to get $\frac{7(x - 2)}{(x + 2)^2(x - 2)}$.3. The third term needs to be multiplied by $(x + 2)$ in both the numerator and denominator to get $\frac{x(x + 2)}{(x + 2)^2(x - 2)}$.Adding these fractions together and simplifying will give you the correct answer, which is $\frac{4x^2 + 5x - 34}{(x + 2)^2(x - 2)}$, matching option C.

Perform the Indicated Operation 5x+2+7x2+4x+4−xx2−4\frac { 5 } { x + 2 } + \frac { 7 } { x ^ { 2 } + 4 x + 4 } - \frac { x } { x ^ { 2 } - 4 }x+25​+x2+4x+47​−x2−4x​

Perform the Indicated Operation $\frac { 5 } { x + 2 } + \frac { 7 } { x ^ { 2 } + 4 x + 4 } - \frac { x } { x ^ { 2 } - 4 }$