Combine and simplify. $\frac { x } { x + 4 } - \frac { 3 } { x - 7 }$
A) $\frac { x ^ { 2 } - 10 x - 12 } { ( x + 4 ) ( x - 7 ) }$
B) $\frac { x ( x - 11 ) } { ( x + 3 ) }$
C) $\frac { x ( x - 7 ) } { ( x + 7 ) ( x - 4 ) }$
D) $\frac { x ^ { 2 } - 7 } { ( x + 3 ) ( x - 4 ) }$
E) $\frac { x - 3 } { ( x + 4 ) ( x - 7 ) }$

Question

Quizplus · Accepted Answer

To combine and simplify the given expression, we need to find a common denominator for the two fractions. The common denominator will be $(x+4)(x-7)$, so we need to rewrite the given fractions with this denominator. We can do this by multiplying the numerator and denominator of the first fraction by $(x-7)$ and the numerator and denominator of the second fraction by $(x+4)$. This gives us: $$\frac{x(x-7)}{(x+4)(x-7)}-\frac{3(x+4)}{(x+4)(x-7)}$$ Simplifying this expression gives: $$\frac{x(x-7)-3(x+4)}{(x+4)(x-7)}$$ Multiplying out the brackets on the numerator gives: $$\frac{x^2-7x-3x-12}{(x+4)(x-7)}$$ Combining like terms on the numerator gives: $$\frac{x^2-10x-12}{(x+4)(x-7)}$$ Therefore, the answer is A.

Combine and Simplify xx+4−3x−7\frac { x } { x + 4 } - \frac { 3 } { x - 7 }x+4x​−x−73​

Combine and Simplify $\frac { x } { x + 4 } - \frac { 3 } { x - 7 }$