Algebra Examples

$\frac{a x - a y}{5 x^{2} y^{2}} \cdot (- \frac{5 x y}{b y - b x})$

Step 1

Simplify terms.

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Step 1.1

Rewrite using the commutative property of multiplication.

$- \frac{a x - a y}{5 x^{2} y^{2}} \cdot \frac{5 x y}{b y - b x}$

Step 1.2

Cancel the common factor of $5 x y$ .

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Step 1.2.1

Move the leading negative in $- \frac{a x - a y}{5 x^{2} y^{2}}$ into the numerator.

$\frac{- (a x - a y)}{5 x^{2} y^{2}} \cdot \frac{5 x y}{b y - b x}$

Step 1.2.2

Factor $5 x y$ out of $5 x^{2} y^{2}$ .

$\frac{- (a x - a y)}{5 x y (x y)} \cdot \frac{5 x y}{b y - b x}$

Step 1.2.3

Cancel the common factor.

$\frac{- (a x - a y)}{5 x y (x y)} \cdot \frac{5 x y}{b y - b x}$

Step 1.2.4

Rewrite the expression.

$\frac{- (a x - a y)}{x y} \cdot \frac{1}{b y - b x}$

Step 1.3

Multiply $\frac{- (a x - a y)}{x y}$ by $\frac{1}{b y - b x}$ .

$\frac{- (a x - a y)}{x y (b y - b x)}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $a$ out of $a x - a y$ .

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Step 2.1.1

Factor $a$ out of $a x$ .

$\frac{- (a (x) - a y)}{x y (b y - b x)}$

Step 2.1.2

Factor $a$ out of $- a y$ .

$\frac{- (a (x) + a (- 1 y))}{x y (b y - b x)}$

Step 2.1.3

Factor $a$ out of $a (x) + a (- 1 y)$ .

$\frac{- (a (x - 1 y))}{x y (b y - b x)}$

Step 2.2

Rewrite $- 1 y$ as $- y$ .

$\frac{- a (x - y)}{x y (b y - b x)}$

Step 3

Simplify the denominator.

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Step 3.1

Factor $b$ out of $b y - b x$ .

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Step 3.1.1

Factor $b$ out of $b y$ .

$\frac{- a (x - y)}{x y (b (y) - b x)}$

Step 3.1.2

Factor $b$ out of $- b x$ .

$\frac{- a (x - y)}{x y (b (y) + b (- 1 x))}$

Step 3.1.3

Factor $b$ out of $b (y) + b (- 1 x)$ .

$\frac{- a (x - y)}{x y (b (y - 1 x))}$

Step 3.2

Rewrite $- 1 x$ as $- x$ .

$\frac{- a (x - y)}{x y b (y - x)}$

Step 4

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

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Step 4.1

Factor $- 1$ out of $x$ .

$\frac{- a (- 1 (- x) - y)}{x y b (y - x)}$

Step 4.2

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

$\frac{- a (- 1 (- x) - (y))}{x y b (y - x)}$

Step 4.3

Factor $- 1$ out of $- 1 (- x) - (y)$ .

$\frac{- a (- 1 (- x + y))}{x y b (y - x)}$

Step 4.4

Reorder terms.

$\frac{- a (- 1 (- x + y))}{x y b (- x + y)}$

Step 4.5

Cancel the common factor.

$\frac{- a (- 1 (- x + y))}{x y b (- x + y)}$

Step 4.6

Rewrite the expression.

$\frac{- a \cdot (- 1)}{x y b}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $- 1$ .

$\frac{1 a}{x y b}$

Step 5.2

Multiply $a$ by $1$ .

$\frac{a}{x y b}$