Finite Math Examples

$\frac{7 + \frac{21}{x + 7}}{\frac{24}{x + 7} + 8}$

Step 1

Multiply the numerator and denominator of the fraction by $x + 7$ .

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Step 1.1

Multiply $\frac{7 + \frac{21}{x + 7}}{\frac{24}{x + 7} + 8}$ by $\frac{x + 7}{x + 7}$ .

$\frac{x + 7}{x + 7} \cdot \frac{7 + \frac{21}{x + 7}}{\frac{24}{x + 7} + 8}$

Step 1.2

Combine.

$\frac{(x + 7) (7 + \frac{21}{x + 7})}{(x + 7) (\frac{24}{x + 7} + 8)}$

Step 2

Apply the distributive property.

$\frac{(x + 7) \cdot 7 + (x + 7) \frac{21}{x + 7}}{(x + 7) \frac{24}{x + 7} + (x + 7) \cdot 8}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $x + 7$ .

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Step 3.1.1

Cancel the common factor.

$\frac{(x + 7) \cdot 7 + (x + 7) \frac{21}{x + 7}}{(x + 7) \frac{24}{x + 7} + (x + 7) \cdot 8}$

Step 3.1.2

Rewrite the expression.

$\frac{(x + 7) \cdot 7 + 21}{(x + 7) \frac{24}{x + 7} + (x + 7) \cdot 8}$

Step 3.2

Cancel the common factor of $x + 7$ .

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Step 3.2.1

Cancel the common factor.

$\frac{(x + 7) \cdot 7 + 21}{(x + 7) \frac{24}{x + 7} + (x + 7) \cdot 8}$

Step 3.2.2

Rewrite the expression.

$\frac{(x + 7) \cdot 7 + 21}{24 + (x + 7) \cdot 8}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $7$ out of $(x + 7) \cdot 7 + 21$ .

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Step 4.1.1

Factor $7$ out of $(x + 7) \cdot 7$ .

$\frac{7 \cdot (x + 7) + 21}{24 + (x + 7) \cdot 8}$

Step 4.1.2

Factor $7$ out of $21$ .

$\frac{7 \cdot (x + 7) + 7 \cdot 3}{24 + (x + 7) \cdot 8}$

Step 4.1.3

Factor $7$ out of $7 \cdot (x + 7) + 7 \cdot 3$ .

$\frac{7 (x + 7 + 3)}{24 + (x + 7) \cdot 8}$

Step 4.2

Add $7$ and $3$ .

$\frac{7 (x + 10)}{24 + (x + 7) \cdot 8}$

Step 5

Simplify the denominator.

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Step 5.1

Apply the distributive property.

$\frac{7 (x + 10)}{24 + x \cdot 8 + 7 \cdot 8}$

Step 5.2

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

$\frac{7 (x + 10)}{24 + 8 \cdot x + 7 \cdot 8}$

Step 5.3

Multiply $7$ by $8$ .

$\frac{7 (x + 10)}{24 + 8 \cdot x + 56}$

Step 5.4

Add $24$ and $56$ .

$\frac{7 (x + 10)}{8 x + 80}$

Step 5.5

Factor $8$ out of $8 x + 80$ .

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Step 5.5.1

Factor $8$ out of $8 x$ .

$\frac{7 (x + 10)}{8 (x) + 80}$

Step 5.5.2

Factor $8$ out of $80$ .

$\frac{7 (x + 10)}{8 x + 8 \cdot 10}$

Step 5.5.3

Factor $8$ out of $8 x + 8 \cdot 10$ .

$\frac{7 (x + 10)}{8 (x + 10)}$

Step 6

Cancel the common factor of $x + 10$ .

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Step 6.1

Cancel the common factor.

$\frac{7 (x + 10)}{8 (x + 10)}$

Step 6.2

Rewrite the expression.

$\frac{7}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{8}$

Decimal Form:

$0.875$