Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { 7 x - 14 } { 4 - x ^ { 2 } } \cdot \frac { 6 x ^ { 2 } + 7 x + 1 } { 42 x + 7 }$$
A) $\frac { x + 1 } { 2 - x }$

B) $- \frac { 7 ( x + 1 ) } { x + 2 }$

C) $\frac { x + 1 } { x + 2 }$

D) $- \frac { x + 1 } { x + 2 }$

Question

Simplify the rational expression. (Assume the denominator is nonzero.)
-$$\frac { 7 x - 14 } { 4 - x ^ { 2 } } \cdot \frac { 6 x ^ { 2 } + 7 x + 1 } { 42 x + 7 }$$
A) $\frac { x + 1 } { 2 - x }$

B) $- \frac { 7 ( x + 1 ) } { x + 2 }$

C) $\frac { x + 1 } { x + 2 }$

D) $- \frac { x + 1 } { x + 2 }$

Quizplus · Accepted Answer

First, factor each polynomial in the expression:- The numerator of the first fraction, $7x - 14$, factors to $7(x - 2)$.- The denominator of the first fraction, $4 - x^2$, is a difference of squares and factors to $(2 - x)(2 + x)$.- The numerator of the second fraction, $6x^2 + 7x + 1$, factors to $(x + 1)(6x + 1)$.- The denominator of the second fraction, $42x + 7$, factors to $7(6x + 1)$.Substituting these factors back into the original expression gives:$$\frac{7(x - 2)}{(2 - x)(2 + x)} \cdot \frac{(x + 1)(6x + 1)}{7(6x + 1)}$$Notice that $(2 - x)$ is $-(x - 2)$, and $(6x + 1)$ cancels out:$$\frac{-7(x - 2)}{-(x - 2)(2 + x)} \cdot \frac{(x + 1)}{7}$$Simplifying further, we get:$$\frac{-1(x + 1)}{(x + 2)}$$Which simplifies to:$$-\frac{x + 1}{x + 2}$$Therefore, the correct answer is D) $- \frac { x + 1 } { x + 2 }$.

Simplify the Rational Expression 7x−144−x2⋅6x2+7x+142x+7\frac { 7 x - 14 } { 4 - x ^ { 2 } } \cdot \frac { 6 x ^ { 2 } + 7 x + 1 } { 42 x + 7 }4−x27x−14​⋅42x+76x2+7x+1​

Simplify the Rational Expression $\frac { 7 x - 14 } { 4 - x ^ { 2 } } \cdot \frac { 6 x ^ { 2 } + 7 x + 1 } { 42 x + 7 }$