Question

In the following exercises, perform indicated operations.

$\frac{x-3}{x+6}-\frac{x}{x+3}$

Short answer

The resultant expression is$\frac{-3(3+2x)}{(x+6)(x+3)}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{x-3}{x+6}-\frac{x}{x+3}$.

Step 2. Express with common denominator  

• The LCD of the terms of obtained expression is $(x+6)(x+3)$.
• Multiply the numerator and denominator of first term by $(x+3)$and second term by $(x+6)$.

role="math" localid="1645432382208" $\frac{(x-3)(x+3)}{(x+6)(x+3)}-\frac{x(x+6)}{(x+3)(x+6)}=\frac{x^2-9}{(x+6)(x+3)}-\frac{x^2+6x}{(x+3)(x+6)}$

Step 3. Simplify

• As the denominator is the same for both the terms, perform subtraction in the numerator and place it over the common denominator.

$\frac{x^2-9-x^2-6x}{(x+6)(x+3)}=\frac{-9-6x}{(x+6)(x+3)}$

• Factor the numerator and express it in the lowest terms possible.

$\frac{-3(3+2x)}{(x+6)(x+3)}$

• So, the resultant expression is $\frac{-3(3+2x)}{(x+6)(x+3)}$.