Basic Math Examples

$\frac{\frac{b - a}{72 a - 45 b}}{\frac{a - b}{64 a - 40 b}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{b - a}{72 a - 45 b} \cdot \frac{64 a - 40 b}{a - b}$

Step 2

Factor $9$ out of $72 a - 45 b$ .

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Step 2.1

Factor $9$ out of $72 a$ .

$\frac{b - a}{9 (8 a) - 45 b} \cdot \frac{64 a - 40 b}{a - b}$

Step 2.2

Factor $9$ out of $- 45 b$ .

$\frac{b - a}{9 (8 a) + 9 (- 5 b)} \cdot \frac{64 a - 40 b}{a - b}$

Step 2.3

Factor $9$ out of $9 (8 a) + 9 (- 5 b)$ .

$\frac{b - a}{9 (8 a - 5 b)} \cdot \frac{64 a - 40 b}{a - b}$

Step 3

Factor $8$ out of $64 a - 40 b$ .

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Step 3.1

Factor $8$ out of $64 a$ .

$\frac{b - a}{9 (8 a - 5 b)} \cdot \frac{8 (8 a) - 40 b}{a - b}$

Step 3.2

Factor $8$ out of $- 40 b$ .

$\frac{b - a}{9 (8 a - 5 b)} \cdot \frac{8 (8 a) + 8 (- 5 b)}{a - b}$

Step 3.3

Factor $8$ out of $8 (8 a) + 8 (- 5 b)$ .

$\frac{b - a}{9 (8 a - 5 b)} \cdot \frac{8 (8 a - 5 b)}{a - b}$

Step 4

Cancel the common factor of $8 a - 5 b$ .

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Step 4.1

Factor $8 a - 5 b$ out of $9 (8 a - 5 b)$ .

$\frac{b - a}{(8 a - 5 b) \cdot 9} \cdot \frac{8 (8 a - 5 b)}{a - b}$

Step 4.2

Factor $8 a - 5 b$ out of $8 (8 a - 5 b)$ .

$\frac{b - a}{(8 a - 5 b) \cdot 9} \cdot \frac{(8 a - 5 b) \cdot 8}{a - b}$

Step 4.3

Cancel the common factor.

$\frac{b - a}{(8 a - 5 b) \cdot 9} \cdot \frac{(8 a - 5 b) \cdot 8}{a - b}$

Step 4.4

Rewrite the expression.

$\frac{b - a}{9} \cdot \frac{8}{a - b}$

Step 5

Multiply $\frac{b - a}{9}$ by $\frac{8}{a - b}$ .

$\frac{(b - a) \cdot 8}{9 (a - b)}$

Step 6

Cancel the common factor of $b - a$ and $a - b$ .

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Step 6.1

Factor $- 1$ out of $b$ .

$\frac{(- 1 (- b) - a) \cdot 8}{9 (a - b)}$

Step 6.2

Factor $- 1$ out of $- a$ .

$\frac{(- 1 (- b) - (a)) \cdot 8}{9 (a - b)}$

Step 6.3

Factor $- 1$ out of $- 1 (- b) - (a)$ .

$\frac{- 1 (- b + a) \cdot 8}{9 (a - b)}$

Step 6.4

Reorder terms.

$\frac{- 1 (a - b) \cdot 8}{9 (a - b)}$

Step 6.5

Cancel the common factor.

$\frac{- 1 (a - b) \cdot 8}{9 (a - b)}$

Step 6.6

Rewrite the expression.

$\frac{- 1 \cdot 8}{9}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $- 1$ by $8$ .

$\frac{- 8}{9}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{8}{9}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{8}{9}$

Decimal Form:

$- 0.\overline{8}$