Algebra Examples

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

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $x^{a}$ and $x^{a - 1}$ .

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Step 1.1.1

Factor $x^{a - 1}$ out of $x^{a} y^{b - 1}$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $x^{a - 1}$ out of $x^{a - 1} y^{b}$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.2

Cancel the common factor of $y^{b - 1}$ and $y^{b}$ .

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Step 1.2.1

Factor $y^{b}$ out of $x^{a - (a - 1)} y^{b - 1}$ .

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Multiply by $1$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 1.2.2.4

Divide $x^{a - (a - 1)} y^{- 1}$ by $1$ .

$x^{a - (a - 1)} y^{- 1}$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$x^{a - a - - 1} y^{- 1}$

Step 2.2

Multiply $- 1$ by $- 1$ .

$x^{a - a + 1} y^{- 1}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $a$ from $a$ .

$x^{0 + 1} y^{- 1}$

Step 3.2

Add $0$ and $1$ .

$x^{1} y^{- 1}$

Step 4

Simplify.

$x y^{- 1}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x \frac{1}{y}$

Step 6

Combine $x$ and $\frac{1}{y}$ .

$\frac{x}{y}$