Perform the operation and simplify the result if possible. $\frac { 2 x + 2 } { x - 5 } - \frac { x - 17 } { 5 - x }$
A) $\frac { 17 x + 2 } { x - 5 }$
B) $\frac { 2 x + 17 } { x - 5 }$
C) $\frac { 2 x + 17 } { 5 - x }$
D) 3
E) 2

Question

Quizplus · Accepted Answer

The second fraction can be rewritten as $-\frac{x-17}{x-5}$ because $5-x = -(x-5)$. The expression becomes $\frac{2x+2}{x-5} + \frac{x-17}{x-5}$. Combine the fractions: $\frac{(2x+2) + (x-17)}{x-5} = \frac{3x-15}{x-5}$. Simplify: $\frac{3(x-5)}{x-5} = 3$.

Perform the Operation and Simplify the Result If Possible 2x+2x−5−x−175−x\frac { 2 x + 2 } { x - 5 } - \frac { x - 17 } { 5 - x }x−52x+2​−5−xx−17​

Perform the Operation and Simplify the Result If Possible $\frac { 2 x + 2 } { x - 5 } - \frac { x - 17 } { 5 - x }$