Finite Math Examples

$\frac{\frac{1}{x} + \frac{5}{x + 1}}{\frac{8}{x + 1} - \frac{7}{x + 1}}$

Step 1

Multiply the numerator and denominator of the fraction by $x (x + 1)$ .

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Step 1.1

Multiply $\frac{\frac{1}{x} + \frac{5}{x + 1}}{\frac{8}{x + 1} - \frac{7}{x + 1}}$ by $\frac{x (x + 1)}{x (x + 1)}$ .

$\frac{x (x + 1)}{x (x + 1)} \cdot \frac{\frac{1}{x} + \frac{5}{x + 1}}{\frac{8}{x + 1} - \frac{7}{x + 1}}$

Step 1.2

Combine.

$\frac{x (x + 1) (\frac{1}{x} + \frac{5}{x + 1})}{x (x + 1) (\frac{8}{x + 1} - \frac{7}{x + 1})}$

Step 2

Apply the distributive property.

$\frac{x (x + 1) \frac{1}{x} + x (x + 1) \frac{5}{x + 1}}{x (x + 1) \frac{8}{x + 1} + x (x + 1) (- \frac{7}{x + 1})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $x$ .

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Step 3.1.1

Cancel the common factor.

$\frac{x (x + 1) \frac{1}{x} + x (x + 1) \frac{5}{x + 1}}{x (x + 1) \frac{8}{x + 1} + x (x + 1) (- \frac{7}{x + 1})}$

Step 3.1.2

Rewrite the expression.

$\frac{x + 1 + x (x + 1) \frac{5}{x + 1}}{x (x + 1) \frac{8}{x + 1} + x (x + 1) (- \frac{7}{x + 1})}$

Step 3.2

Cancel the common factor of $x + 1$ .

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Step 3.2.1

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

$\frac{x + 1 + (x + 1) x \frac{5}{x + 1}}{x (x + 1) \frac{8}{x + 1} + x (x + 1) (- \frac{7}{x + 1})}$

Step 3.2.2

Cancel the common factor.

$\frac{x + 1 + (x + 1) x \frac{5}{x + 1}}{x (x + 1) \frac{8}{x + 1} + x (x + 1) (- \frac{7}{x + 1})}$

Step 3.2.3

Rewrite the expression.

$\frac{x + 1 + x \cdot 5}{x (x + 1) \frac{8}{x + 1} + x (x + 1) (- \frac{7}{x + 1})}$

Step 3.3

Cancel the common factor of $x + 1$ .

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Step 3.3.1

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

$\frac{x + 1 + x \cdot 5}{(x + 1) x \frac{8}{x + 1} + x (x + 1) (- \frac{7}{x + 1})}$

Step 3.3.2

Cancel the common factor.

$\frac{x + 1 + x \cdot 5}{(x + 1) x \frac{8}{x + 1} + x (x + 1) (- \frac{7}{x + 1})}$

Step 3.3.3

Rewrite the expression.

$\frac{x + 1 + x \cdot 5}{x \cdot 8 + x (x + 1) (- \frac{7}{x + 1})}$

Step 3.4

Cancel the common factor of $x + 1$ .

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Step 3.4.1

Move the leading negative in $- \frac{7}{x + 1}$ into the numerator.

$\frac{x + 1 + x \cdot 5}{x \cdot 8 + x (x + 1) \frac{- 7}{x + 1}}$

Step 3.4.2

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

$\frac{x + 1 + x \cdot 5}{x \cdot 8 + (x + 1) x \frac{- 7}{x + 1}}$

Step 3.4.3

Cancel the common factor.

$\frac{x + 1 + x \cdot 5}{x \cdot 8 + (x + 1) x \frac{- 7}{x + 1}}$

Step 3.4.4

Rewrite the expression.

$\frac{x + 1 + x \cdot 5}{x \cdot 8 + x \cdot - 7}$

Step 4

Simplify the numerator.

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Step 4.1

Move $5$ to the left of $x$ .

$\frac{x + 1 + 5 \cdot x}{x \cdot 8 + x \cdot - 7}$

Step 4.2

Add $x$ and $5 x$ .

$\frac{6 x + 1}{x \cdot 8 + x \cdot - 7}$

Step 5

Simplify the denominator.

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Step 5.1

Move $8$ to the left of $x$ .

$\frac{6 x + 1}{8 \cdot x + x \cdot - 7}$

Step 5.2

Move $- 7$ to the left of $x$ .

$\frac{6 x + 1}{8 x - 7 \cdot x}$

Step 5.3

Subtract $7 x$ from $8 x$ .

$\frac{6 x + 1}{x}$