Simplify (6x^2y^3(x+3y))/(18x^2y(x+3y)^2)

$\frac{6 x^{2} y^{3} (x + 3 y)}{18 x^{2} y {(x + 3 y)}^{2}}$

Step 1

Cancel the common factor of $6$ and $18$ .

Factor $6$ out of $6 x^{2} y^{3} (x + 3 y)$ .

$\frac{6 (x^{2} y^{3} (x + 3 y))}{18 x^{2} y {(x + 3 y)}^{2}}$

Cancel the common factors.

Factor $6$ out of $18 x^{2} y {(x + 3 y)}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x^{2} y^{3} (x + 3 y)}{3 x^{2} y {(x + 3 y)}^{2}}$

Step 2

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{x^{2} y^{3} (x + 3 y)}{3 x^{2} y {(x + 3 y)}^{2}}$

Rewrite the expression.

$\frac{y^{3} (x + 3 y)}{3 y {(x + 3 y)}^{2}}$

Step 3

Cancel the common factor of $y^{3}$ and $y$ .

Factor $y$ out of $y^{3} (x + 3 y)$ .

$\frac{y (y^{2} (x + 3 y))}{3 y {(x + 3 y)}^{2}}$

Cancel the common factors.

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

$\frac{y (y^{2} (x + 3 y))}{y (3 {(x + 3 y)}^{2})}$

Cancel the common factor.

$\frac{y (y^{2} (x + 3 y))}{y (3 {(x + 3 y)}^{2})}$

Rewrite the expression.

$\frac{y^{2} (x + 3 y)}{3 {(x + 3 y)}^{2}}$

Step 4

Cancel the common factor of $x + 3 y$ and ${(x + 3 y)}^{2}$ .

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

$\frac{(x + 3 y) y^{2}}{3 {(x + 3 y)}^{2}}$

Cancel the common factors.

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

$\frac{(x + 3 y) y^{2}}{(x + 3 y) (3 (x + 3 y))}$

Cancel the common factor.

$\frac{(x + 3 y) y^{2}}{(x + 3 y) (3 (x + 3 y))}$

Rewrite the expression.

$\frac{y^{2}}{3 (x + 3 y)}$