Algebra Examples

$\frac{x - 6}{x + 3} \cdot \frac{y}{x - 6} = x - 2$

Step 1

Simplify $\frac{x - 6}{x + 3} \cdot \frac{y}{x - 6}$ .

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Step 1.1

Cancel the common factor of $x - 6$ .

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Step 1.1.1

Cancel the common factor.

$\frac{x - 6}{x + 3} \cdot \frac{y}{x - 6} = x - 2$

Step 1.1.2

Rewrite the expression.

$\frac{1}{x + 3} \cdot y = x - 2$

Step 1.2

Combine $\frac{1}{x + 3}$ and $y$ .

$\frac{y}{x + 3} = x - 2$

Step 2

Multiply both sides by $x + 3$ .

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

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $x + 3$ .

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Step 3.1.1.1

Cancel the common factor.

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

Step 3.1.1.2

Rewrite the expression.

$y = (x - 2) (x + 3)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $(x - 2) (x + 3)$ .

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Step 3.2.1.1

Expand $(x - 2) (x + 3)$ using the FOIL Method.

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Step 3.2.1.1.1

Apply the distributive property.

$y = x (x + 3) - 2 (x + 3)$

Step 3.2.1.1.2

Apply the distributive property.

$y = x \cdot x + x \cdot 3 - 2 (x + 3)$

Step 3.2.1.1.3

Apply the distributive property.

$y = x \cdot x + x \cdot 3 - 2 x - 2 \cdot 3$

Step 3.2.1.2

Simplify and combine like terms.

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Step 3.2.1.2.1

Simplify each term.

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Step 3.2.1.2.1.1

Multiply $x$ by $x$ .

$y = x^{2} + x \cdot 3 - 2 x - 2 \cdot 3$

Step 3.2.1.2.1.2

Move $3$ to the left of $x$ .

$y = x^{2} + 3 \cdot x - 2 x - 2 \cdot 3$

Step 3.2.1.2.1.3

Multiply $- 2$ by $3$ .

$y = x^{2} + 3 x - 2 x - 6$

Step 3.2.1.2.2

Subtract $2 x$ from $3 x$ .

$y = x^{2} + x - 6$