Simplify (8a+4b)/(2ab+b^2-2ad-bd)

$\frac{8 a + 4 b}{2 a b + b^{2} - 2 a d - b d}$

Step 1

Factor $4$ out of $8 a + 4 b$ .

Factor $4$ out of $8 a$ .

$\frac{4 (2 a) + 4 b}{2 a b + b^{2} - 2 a d - b d}$

Factor $4$ out of $4 b$ .

$\frac{4 (2 a) + 4 (b)}{2 a b + b^{2} - 2 a d - b d}$

Factor $4$ out of $4 (2 a) + 4 (b)$ .

$\frac{4 (2 a + b)}{2 a b + b^{2} - 2 a d - b d}$

Step 2

Simplify the denominator.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$\frac{4 (2 a + b)}{(2 a b + b^{2}) - 2 a d - b d}$

Factor out the greatest common factor (GCF) from each group.

$\frac{4 (2 a + b)}{b (2 a + b) - d (2 a + b)}$

Factor the polynomial by factoring out the greatest common factor, $2 a + b$ .

$\frac{4 (2 a + b)}{(2 a + b) (b - d)}$

Step 3

Cancel the common factor of $2 a + b$ .

Cancel the common factor.

$\frac{4 (2 a + b)}{(2 a + b) (b - d)}$

Rewrite the expression.

$\frac{4}{b - d}$