Question

Subtract$\frac{4d}{d^2-81}-\frac{2}{d+9}$.

Short answer

The difference is$\frac{2}{d-9}$.

Step-by-step solution

Given Information    

The Given expression is$\frac{4d}{d^2-81}-\frac{2}{d+9}$.

Find the LCD of denominators.    

Factor the denominators.

$d^2-81=(d+9)(d-9)$

$d+9=(d+9)$

LCD$=(d+9)(d-9)$

Rewrite the expression in factored form.

$=\frac{4d}{(d+9)(d-9)}-\frac{2}{d+9}$

Rewrite each fraction as an equivalent fraction with the LCD.   

$=\frac{4d}{(d+9)(d-9)}-\frac{2(d-9)}{(d+9)(d-9)}$

Simplify numerators.

$=\frac{4d}{(d+9)(d-9)}-\frac{2d-18}{(d+9)(d-9)}$

Subtract and simplify the numerator.   

Take common denominator.

$=\frac{4d-(2d-18)}{(d+9)(d-9)}$

$=\frac{4d-2d+18}{(d+9)(d-9)}$

Simplify.

$=\frac{2d+18}{(d+9)(d-9)}$

$=\frac{2(d+9)}{(d+9)(d-9)}$

$=\frac{2}{d-9}$