Precalculus Examples

$\frac{\frac{4}{x - 2} + 4}{\frac{3}{x - 2} + 3}$

Step 1

Multiply the numerator and denominator of the fraction by $x - 2$ .

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Step 1.1

Multiply $\frac{\frac{4}{x - 2} + 4}{\frac{3}{x - 2} + 3}$ by $\frac{x - 2}{x - 2}$ .

$\frac{x - 2}{x - 2} \cdot \frac{\frac{4}{x - 2} + 4}{\frac{3}{x - 2} + 3}$

Step 1.2

Combine.

$\frac{(x - 2) (\frac{4}{x - 2} + 4)}{(x - 2) (\frac{3}{x - 2} + 3)}$

Step 2

Apply the distributive property.

$\frac{(x - 2) \frac{4}{x - 2} + (x - 2) \cdot 4}{(x - 2) \frac{3}{x - 2} + (x - 2) \cdot 3}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $x - 2$ .

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Step 3.1.1

Cancel the common factor.

$\frac{(x - 2) \frac{4}{x - 2} + (x - 2) \cdot 4}{(x - 2) \frac{3}{x - 2} + (x - 2) \cdot 3}$

Step 3.1.2

Rewrite the expression.

$\frac{4 + (x - 2) \cdot 4}{(x - 2) \frac{3}{x - 2} + (x - 2) \cdot 3}$

Step 3.2

Cancel the common factor of $x - 2$ .

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Step 3.2.1

Cancel the common factor.

$\frac{4 + (x - 2) \cdot 4}{(x - 2) \frac{3}{x - 2} + (x - 2) \cdot 3}$

Step 3.2.2

Rewrite the expression.

$\frac{4 + (x - 2) \cdot 4}{3 + (x - 2) \cdot 3}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{4 + x \cdot 4 - 2 \cdot 4}{3 + (x - 2) \cdot 3}$

Step 4.2

Move $4$ to the left of $x$ .

$\frac{4 + 4 \cdot x - 2 \cdot 4}{3 + (x - 2) \cdot 3}$

Step 4.3

Multiply $- 2$ by $4$ .

$\frac{4 + 4 \cdot x - 8}{3 + (x - 2) \cdot 3}$

Step 4.4

Subtract $8$ from $4$ .

$\frac{4 x - 4}{3 + (x - 2) \cdot 3}$

Step 4.5

Factor $4$ out of $4 x - 4$ .

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Step 4.5.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 4}{3 + (x - 2) \cdot 3}$

Step 4.5.2

Factor $4$ out of $- 4$ .

$\frac{4 (x) + 4 (- 1)}{3 + (x - 2) \cdot 3}$

Step 4.5.3

Factor $4$ out of $4 (x) + 4 (- 1)$ .

$\frac{4 (x - 1)}{3 + (x - 2) \cdot 3}$

Step 5

Simplify the denominator.

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Step 5.1

Apply the distributive property.

$\frac{4 (x - 1)}{3 + x \cdot 3 - 2 \cdot 3}$

Step 5.2

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

$\frac{4 (x - 1)}{3 + 3 \cdot x - 2 \cdot 3}$

Step 5.3

Multiply $- 2$ by $3$ .

$\frac{4 (x - 1)}{3 + 3 \cdot x - 6}$

Step 5.4

Subtract $6$ from $3$ .

$\frac{4 (x - 1)}{3 x - 3}$

Step 5.5

Factor $3$ out of $3 x - 3$ .

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Step 5.5.1

Factor $3$ out of $3 x$ .

$\frac{4 (x - 1)}{3 (x) - 3}$

Step 5.5.2

Factor $3$ out of $- 3$ .

$\frac{4 (x - 1)}{3 (x) + 3 (- 1)}$

Step 5.5.3

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

$\frac{4 (x - 1)}{3 (x - 1)}$

Step 6

Cancel the common factor of $x - 1$ .

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Step 6.1

Cancel the common factor.

$\frac{4 (x - 1)}{3 (x - 1)}$

Step 6.2

Rewrite the expression.

$\frac{4}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$