Subtract.
-$$\frac { 2 x ^ { 2 } + 20 } { x ^ { 2 } + 5 x - 6 } - \frac { 13 x } { x ^ { 2 } + 5 x - 6 }$$
A) $\frac { ( x - 4 ) ( 2 x - 5 ) } { ( x + 6 ) ( x - 1 ) }$
B) $\frac { ( x - 4 ) ( 2 x + 5 ) } { ( x + 6 ) ( x - 1 ) }$
C) $\frac { ( x + 4 ) ( 2 x + 5 ) } { ( x + 6 ) ( x - 1 ) }$
D) $\frac { 2 x - 5 } { x - 1 }$

Question

Quizplus · Accepted Answer

To subtract the two fractions, we need a common denominator. 
$$x^2 + 5x - 6 = (x + 6)(x - 1)$$
So the two fractions become:
$$\frac{2x^2 + 20}{(x + 6)(x - 1)} - \frac{13x}{(x + 6)(x - 1)}$$
To combine them, we just subtract the numerators:
$$\frac{2x^2 + 20 - 13x}{(x + 6)(x - 1)}$$
Simplifying the numerator gives us:
$$2x^2 - 13x + 20 = (2x - 5)(x - 4)$$
So the final answer is:
$$\frac{(2x - 5)(x - 4)}{(x + 6)(x - 1)} = \boxed{\text{(A)}}$$

Subtract - 2x2+20x2+5x−6−13xx2+5x−6\frac { 2 x ^ { 2 } + 20 } { x ^ { 2 } + 5 x - 6 } - \frac { 13 x } { x ^ { 2 } + 5 x - 6 }x2+5x−62x2+20​−x2+5x−613x​

Subtract
- $\frac { 2 x ^ { 2 } + 20 } { x ^ { 2 } + 5 x - 6 } - \frac { 13 x } { x ^ { 2 } + 5 x - 6 }$