Simplify (8x(3x+5)(x+7)^2)/(32x(x+7)(3x-5))

$\frac{8 x (3 x + 5) {(x + 7)}^{2}}{32 x (x + 7) (3 x - 5)}$

Step 1

Cancel the common factor of $8$ and $32$ .

Factor $8$ out of $8 x (3 x + 5) {(x + 7)}^{2}$ .

$\frac{8 ((x (3 x + 5)) {(x + 7)}^{2})}{32 x (x + 7) (3 x - 5)}$

Cancel the common factors.

Factor $8$ out of $32 x (x + 7) (3 x - 5)$ .

$\frac{8 ((x (3 x + 5)) {(x + 7)}^{2})}{8 (4 x (x + 7) (3 x - 5))}$

Cancel the common factor.

$\frac{8 ((x (3 x + 5)) {(x + 7)}^{2})}{8 (4 x (x + 7) (3 x - 5))}$

Rewrite the expression.

$\frac{(x (3 x + 5)) {(x + 7)}^{2}}{4 x (x + 7) (3 x - 5)}$

Step 2

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x (3 x + 5) {(x + 7)}^{2}}{4 x (x + 7) (3 x - 5)}$

Rewrite the expression.

$\frac{(3 x + 5) {(x + 7)}^{2}}{(4 (x + 7)) (3 x - 5)}$

Step 3

Cancel the common factor of ${(x + 7)}^{2}$ and $x + 7$ .

Factor $x + 7$ out of $(3 x + 5) {(x + 7)}^{2}$ .

$\frac{(x + 7) ((3 x + 5) (x + 7))}{(4 (x + 7)) (3 x - 5)}$

Cancel the common factors.

Factor $x + 7$ out of $(4 (x + 7)) (3 x - 5)$ .

$\frac{(x + 7) ((3 x + 5) (x + 7))}{(x + 7) ((4) (3 x - 5))}$

Cancel the common factor.

$\frac{(x + 7) ((3 x + 5) (x + 7))}{(x + 7) ((4) (3 x - 5))}$

Rewrite the expression.

$\frac{(3 x + 5) (x + 7)}{(4) (3 x - 5)}$

$\frac{(3 x + 5) (x + 7)}{4 (3 x - 5)}$