Algebra Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $x + 3$ .

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Step 1.1

Multiply $\frac{x - \frac{x}{x + 3}}{x + 2}$ by $\frac{x + 3}{x + 3}$ .

$\frac{x + 3}{x + 3} \cdot \frac{x - \frac{x}{x + 3}}{x + 2}$

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Cancel the common factor of $x + 3$ .

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Step 3.1

Move the leading negative in $- \frac{x}{x + 3}$ into the numerator.

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

Simplify the numerator.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

Factor $x$ out of $- x$ .

$\frac{x (x + 3) + x \cdot - 1}{(x + 3) x + (x + 3) \cdot 2}$

Step 4.1.3

Factor $x$ out of $x (x + 3) + x \cdot - 1$ .

$\frac{x (x + 3 - 1)}{(x + 3) x + (x + 3) \cdot 2}$

Step 4.2

Subtract $1$ from $3$ .

$\frac{x (x + 2)}{(x + 3) x + (x + 3) \cdot 2}$

Step 5

Simplify terms.

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Step 5.1

Factor $x + 3$ out of $(x + 3) x + (x + 3) \cdot 2$ .

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Step 5.1.1

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

$\frac{x (x + 2)}{(x + 3) (x) + (x + 3) \cdot 2}$

Step 5.1.2

Factor $x + 3$ out of $(x + 3) \cdot 2$ .

$\frac{x (x + 2)}{(x + 3) (x) + (x + 3) (2)}$

Step 5.1.3

Factor $x + 3$ out of $(x + 3) (x) + (x + 3) (2)$ .

$\frac{x (x + 2)}{(x + 3) (x + 2)}$

Step 5.2

Cancel the common factor of $x + 2$ .

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Step 5.2.1

Cancel the common factor.

$\frac{x (x + 2)}{(x + 3) (x + 2)}$

Step 5.2.2

Rewrite the expression.

$\frac{x}{x + 3}$