Simplify the expression.
-$\frac { 36 - x ^ { 2 } } { x ^ { 2 } - 13 x + 42 }$
A) $- \frac { x - 6 } { x - 7 }$
B) $- \frac { x + 6 } { x + 7 }$
C) $- \frac { x + 6 } { x - 7 }$
D) $\frac { x + 6 } { x - 7 }$

Question

Quizplus · Accepted Answer

The expression can be simplified by factoring both the numerator and the denominator. The numerator $36 - x^2$ is a difference of squares and factors to $(6 - x)(6 + x)$. The denominator $x^2 - 13x + 42$ factors to $(x - 6)(x - 7)$. Simplifying the expression by canceling the common factor $(x - 6)$ gives $-\frac{x + 6}{x - 7}$.

Simplify the Expression 36−x2x2−13x+42\frac { 36 - x ^ { 2 } } { x ^ { 2 } - 13 x + 42 }x2−13x+4236−x2​

Simplify the Expression $\frac { 36 - x ^ { 2 } } { x ^ { 2 } - 13 x + 42 }$