# How do you simplify (9m²-16n²) /( 6m-8n)?

May 19, 2018

$\frac{9 {m}^{2} - 16 {n}^{2}}{6 m - 8 n}$ = $\frac{3 m + 4 n}{2}$

#### Explanation:

First factorize $9 {m}^{2} - 16 {n}^{2}$

$9 {m}^{2} - 16 {n}^{2}$ = $\left(3 m - 4 n\right) \left(3 m + 4 n\right)$

Check:
$\left(3 m - 4 n\right) \left(3 m + 4 n\right)$ = $9 {m}^{2} + 12 m n - 12 m n - 16 {n}^{2}$
$\left(3 m - 4 n\right) \left(3 m + 4 n\right)$ = $9 {m}^{2} + \cancel{12 m n - 12 m n} - 16 {n}^{2}$
$\left(3 m - 4 n\right) \left(3 m + 4 n\right)$ = $9 {m}^{2} - 16 {n}^{2}$

$\frac{9 {m}^{2} - 16 {n}^{2}}{6 m - 8 n}$ = $\frac{\left(3 m - 4 n\right) \left(3 m + 4 n\right)}{6 m - 8 n}$

$\frac{9 {m}^{2} - 16 {n}^{2}}{6 m - 8 n}$ = $\frac{\left(3 m - 4 n\right) \left(3 m + 4 n\right)}{2 \left(3 m - 4 n\right)}$

$\frac{9 {m}^{2} - 16 {n}^{2}}{6 m - 8 n}$ = (cancel((3m-4n))(3m+4n))/(2(cancel(3m-4n))

$\frac{9 {m}^{2} - 16 {n}^{2}}{6 m - 8 n}$ = $\frac{3 m + 4 n}{2}$