Basic Math Examples

$\frac{b^{2} - a^{2}}{2 a^{2} - 2 b^{2}}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = b$ and $b = a$ .

$\frac{(b + a) (b - a)}{2 a^{2} - 2 b^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Factor $2$ out of $2 a^{2} - 2 b^{2}$ .

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Step 2.1.1

Factor $2$ out of $2 a^{2}$ .

$\frac{(b + a) (b - a)}{2 (a^{2}) - 2 b^{2}}$

Step 2.1.2

Factor $2$ out of $- 2 b^{2}$ .

$\frac{(b + a) (b - a)}{2 (a^{2}) + 2 (- b^{2})}$

Step 2.1.3

Factor $2$ out of $2 (a^{2}) + 2 (- b^{2})$ .

$\frac{(b + a) (b - a)}{2 (a^{2} - b^{2})}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

$\frac{(b + a) (b - a)}{2 (a + b) (a - b)}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

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

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Step 3.1.1

Reorder terms.

$\frac{(a + b) (b - a)}{2 (a + b) (a - b)}$

Step 3.1.2

Cancel the common factor.

$\frac{(a + b) (b - a)}{2 (a + b) (a - b)}$

Step 3.1.3

Rewrite the expression.

$\frac{b - a}{2 (a - b)}$

Step 3.2

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

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Step 3.2.1

Factor $- 1$ out of $b$ .

$\frac{- 1 (- b) - a}{2 (a - b)}$

Step 3.2.2

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

$\frac{- 1 (- b) - (a)}{2 (a - b)}$

Step 3.2.3

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

$\frac{- 1 (- b + a)}{2 (a - b)}$

Step 3.2.4

Reorder terms.

$\frac{- 1 (a - b)}{2 (a - b)}$

Step 3.2.5

Cancel the common factor.

$\frac{- 1 (a - b)}{2 (a - b)}$

Step 3.2.6

Rewrite the expression.

$\frac{- 1}{2}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$