Simplify (16x^2y(y+x))/(12xy(x+y))

$\frac{16 x^{2} y (y + x)}{12 x y (x + y)}$

Step 1

Cancel the common factor of $16$ and $12$ .

Factor $4$ out of $16 x^{2} y (y + x)$ .

$\frac{4 (4 x^{2} y (y + x))}{12 x y (x + y)}$

Cancel the common factors.

Factor $4$ out of $12 x y (x + y)$ .

$\frac{4 (4 x^{2} y (y + x))}{4 (3 x y (x + y))}$

Cancel the common factor.

$\frac{4 (4 x^{2} y (y + x))}{4 (3 x y (x + y))}$

Rewrite the expression.

$\frac{4 x^{2} y (y + x)}{3 x y (x + y)}$

$\frac{4 x^{2} y (y + x)}{3 x y (x + y)}$

$\frac{4 x^{2} y (y + x)}{3 x y (x + y)}$

Step 2

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

Factor $x$ out of $4 x^{2} y (y + x)$ .

$\frac{x (4 x y (y + x))}{3 x y (x + y)}$

Cancel the common factors.

Factor $x$ out of $3 x y (x + y)$ .

$\frac{x (4 x y (y + x))}{x (3 y (x + y))}$

Cancel the common factor.

$\frac{x (4 x y (y + x))}{x (3 y (x + y))}$

Rewrite the expression.

$\frac{4 x y (y + x)}{3 y (x + y)}$

$\frac{4 x y (y + x)}{3 y (x + y)}$

$\frac{4 x y (y + x)}{3 y (x + y)}$

Step 3

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{4 x y (y + x)}{3 y (x + y)}$

Rewrite the expression.

$\frac{4 x (y + x)}{3 (x + y)}$

$\frac{4 x (y + x)}{3 (x + y)}$

Step 4

Cancel the common factor of $y + x$ and $x + y$ .

Reorder terms.

$\frac{4 x (x + y)}{3 (x + y)}$

Cancel the common factor.

$\frac{4 x (x + y)}{3 (x + y)}$

Rewrite the expression.

$\frac{4 x}{3}$

$\frac{4 x}{3}$

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