Subtract. Simplify, if possible.
-$\frac { 5 x } { x ^ { 2 } - 5 x + 6 } - \frac { 20 } { x ^ { 2 } - 6 x + 8 }$

A) $\frac { x - 6 } { ( x - 3 ) ( x - 4 ) }$

B) $\frac { 5 } { ( x - 2 ) ( x - 3 ) }$

C)$\frac { 5 ( x - 6 ) } { ( x - 3 ) ( x - 4 ) }$

D) $\frac { 5 x - 20 } { ( x - 2 ) ( x - 3 ) ( x - 4 ) }$

Question

Subtract. Simplify, if possible.
-$\frac { 5 x } { x ^ { 2 } - 5 x + 6 } - \frac { 20 } { x ^ { 2 } - 6 x + 8 }$

A) $\frac { x - 6 } { ( x - 3 ) ( x - 4 ) }$

B) $\frac { 5 } { ( x - 2 ) ( x - 3 ) }$

C)$\frac { 5 ( x - 6 ) } { ( x - 3 ) ( x - 4 ) }$

D) $\frac { 5 x - 20 } { ( x - 2 ) ( x - 3 ) ( x - 4 ) }$

Quizplus · Accepted Answer

First, factor the denominators: $x^2 - 5x + 6 = (x - 2)(x - 3)$ and $x^2 - 6x + 8 = (x - 2)(x - 4)$. To subtract the fractions, find a common denominator, which is $(x - 2)(x - 3)(x - 4)$. Adjust the numerators accordingly to have the same denominator, leading to the subtraction and simplification to $\frac{5(x - 6)}{(x - 3)(x - 4)}$, which matches choice C.

Subtract Simplify, If Possible 5xx2−5x+6−20x2−6x+8\frac { 5 x } { x ^ { 2 } - 5 x + 6 } - \frac { 20 } { x ^ { 2 } - 6 x + 8 }x2−5x+65x​−x2−6x+820​

Subtract Simplify, If Possible $\frac { 5 x } { x ^ { 2 } - 5 x + 6 } - \frac { 20 } { x ^ { 2 } - 6 x + 8 }$