Perform the operations and simplify the result when possible. $\frac { x + 4 } { x + 5 } - \frac { x - 5 } { x + 7 }$
A) $\frac { 11 x + 53 } { ( x + 5 ) ( x + 7 ) }$
B) $\frac { 2 ( 11 x + 53 ) } { ( x + 5 ) ( x + 7 ) }$
C) $\frac { 11 x + 53 } { x + 5 }$
D) $\frac { 53 x + 11 } { ( x + 5 ) ( x + 7 ) }$
E) $\frac { 11 x ^ { 2 } + 53 } { ( x + 5 ) ( x + 7 ) }$

Question

Quizplus · Accepted Answer

To simplify the expression, find a common denominator, which is $(x + 5)(x + 7)$, and then combine the numerators:$$\frac{x + 4}{x + 5} - \frac{x - 5}{x + 7} = \frac{(x + 4)(x + 7) - (x - 5)(x + 5)}{(x + 5)(x + 7)}$$Simplifying the numerator:$$(x^2 + 11x + 28) - (x^2 - 25) = x^2 + 11x + 28 - x^2 + 25 = 11x + 53$$So, the simplified expression is:$$\frac{11x + 53}{(x + 5)(x + 7)}$$

Perform the Operations and Simplify the Result When Possible x+4x+5−x−5x+7\frac { x + 4 } { x + 5 } - \frac { x - 5 } { x + 7 }x+5x+4​−x+7x−5​

Perform the Operations and Simplify the Result When Possible $\frac { x + 4 } { x + 5 } - \frac { x - 5 } { x + 7 }$