Algebra Examples

$\frac{(4 w^{2} - 3 w y) (w + y)}{(3 y - 4 w) (5 w + y)}$

Step 1

Factor $w$ out of $4 w^{2} - 3 w y$ .

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Step 1.1

Factor $w$ out of $4 w^{2}$ .

$\frac{(w (4 w) - 3 w y) (w + y)}{(3 y - 4 w) (5 w + y)}$

Step 1.2

Factor $w$ out of $- 3 w y$ .

$\frac{(w (4 w) + w (- 3 y)) (w + y)}{(3 y - 4 w) (5 w + y)}$

Step 1.3

Factor $w$ out of $w (4 w) + w (- 3 y)$ .

$\frac{w (4 w - 3 y) (w + y)}{(3 y - 4 w) (5 w + y)}$

Step 2

Cancel the common factor of $4 w - 3 y$ and $3 y - 4 w$ .

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Step 2.1

Factor $- 1$ out of $4 w$ .

$\frac{w (- (- 4 w) - 3 y) (w + y)}{(3 y - 4 w) (5 w + y)}$

Step 2.2

Factor $- 1$ out of $- 3 y$ .

$\frac{w (- (- 4 w) - (3 y)) (w + y)}{(3 y - 4 w) (5 w + y)}$

Step 2.3

Factor $- 1$ out of $- (- 4 w) - (3 y)$ .

$\frac{w (- (- 4 w + 3 y)) (w + y)}{(3 y - 4 w) (5 w + y)}$

Step 2.4

Rewrite $- (- 4 w + 3 y)$ as $- 1 (- 4 w + 3 y)$ .

$\frac{w (- 1 (- 4 w + 3 y)) (w + y)}{(3 y - 4 w) (5 w + y)}$

Step 2.5

Reorder terms.

$\frac{w (- 1 (- 4 w + 3 y)) (w + y)}{(- 4 w + 3 y) (5 w + y)}$

Step 2.6

Cancel the common factor.

$\frac{w (- 1 (- 4 w + 3 y)) (w + y)}{(- 4 w + 3 y) (5 w + y)}$

Step 2.7

Rewrite the expression.

$\frac{w \cdot (- 1) (w + y)}{5 w + y}$

Step 3

Factor out negative.

$\frac{- w (w + y)}{5 w + y}$

Step 4

Move the negative in front of the fraction.

$- \frac{w (w + y)}{5 w + y}$