Basic Math Examples

$\frac{\frac{7}{A} + \frac{8}{B}}{8 A + 7 B}$

Step 1

Multiply the numerator and denominator of the fraction by $A B$ .

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Step 1.1

Multiply $\frac{\frac{7}{A} + \frac{8}{B}}{8 A + 7 B}$ by $\frac{A B}{A B}$ .

$\frac{A B}{A B} \cdot \frac{\frac{7}{A} + \frac{8}{B}}{8 A + 7 B}$

Step 1.2

Combine.

$\frac{A B (\frac{7}{A} + \frac{8}{B})}{A B (8 A + 7 B)}$

Step 2

Apply the distributive property.

$\frac{A B \frac{7}{A} + A B \frac{8}{B}}{A B (8 A) + A B (7 B)}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $A$ .

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Step 3.1.1

Factor $A$ out of $A B$ .

$\frac{A (B) \frac{7}{A} + A B \frac{8}{B}}{A B (8 A) + A B (7 B)}$

Step 3.1.2

Cancel the common factor.

$\frac{A B \frac{7}{A} + A B \frac{8}{B}}{A B (8 A) + A B (7 B)}$

Step 3.1.3

Rewrite the expression.

$\frac{B \cdot 7 + A B \frac{8}{B}}{A B (8 A) + A B (7 B)}$

Step 3.2

Cancel the common factor of $B$ .

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Step 3.2.1

Factor $B$ out of $A B$ .

$\frac{B \cdot 7 + B A \frac{8}{B}}{A B (8 A) + A B (7 B)}$

Step 3.2.2

Cancel the common factor.

$\frac{B \cdot 7 + B A \frac{8}{B}}{A B (8 A) + A B (7 B)}$

Step 3.2.3

Rewrite the expression.

$\frac{B \cdot 7 + A \cdot 8}{A B (8 A) + A B (7 B)}$

Step 4

Simplify the numerator.

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Step 4.1

Move $7$ to the left of $B$ .

$\frac{7 \cdot B + A \cdot 8}{A B (8 A) + A B (7 B)}$

Step 4.2

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

$\frac{7 B + 8 A}{A B (8 A) + A B (7 B)}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite using the commutative property of multiplication.

$\frac{7 B + 8 A}{8 A B A + A B (7 B)}$

Step 5.2

Multiply $A$ by $A$ by adding the exponents.

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Step 5.2.1

Move $A$ .

$\frac{7 B + 8 A}{8 (A \cdot A) B + A B (7 B)}$

Step 5.2.2

Multiply $A$ by $A$ .

$\frac{7 B + 8 A}{8 A^{2} B + A B (7 B)}$

Step 5.3

Rewrite using the commutative property of multiplication.

$\frac{7 B + 8 A}{8 A^{2} B + 7 A B \cdot B}$

Step 5.4

Multiply $B$ by $B$ by adding the exponents.

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Step 5.4.1

Move $B$ .

$\frac{7 B + 8 A}{8 A^{2} B + 7 A (B \cdot B)}$

Step 5.4.2

Multiply $B$ by $B$ .

$\frac{7 B + 8 A}{8 A^{2} B + 7 A B^{2}}$

Step 5.5

Factor $A B$ out of $8 A^{2} B + 7 A B^{2}$ .

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Step 5.5.1

Factor $A B$ out of $8 A^{2} B$ .

$\frac{7 B + 8 A}{A B (8 A) + 7 A B^{2}}$

Step 5.5.2

Factor $A B$ out of $7 A B^{2}$ .

$\frac{7 B + 8 A}{A B (8 A) + A B (7 B)}$

Step 5.5.3

Factor $A B$ out of $A B (8 A) + A B (7 B)$ .

$\frac{7 B + 8 A}{A B (8 A + 7 B)}$

Step 6

Cancel the common factor of $7 B + 8 A$ and $8 A + 7 B$ .

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Step 6.1

Reorder terms.

$\frac{8 A + 7 B}{A B (8 A + 7 B)}$

Step 6.2

Cancel the common factor.

$\frac{8 A + 7 B}{A B (8 A + 7 B)}$

Step 6.3

Rewrite the expression.

$\frac{1}{A B}$