Algebra Examples

$\frac{3 a - 1}{a^{2} - b^{2}} - \frac{3 b - 1}{a^{2} - b^{2}}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{3 a - 1 - (3 b - 1)}{a^{2} - b^{2}}$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\frac{3 a - 1 - (3 b) - - 1}{a^{2} - b^{2}}$

Step 1.2.2

Multiply $3$ by $- 1$ .

$\frac{3 a - 1 - 3 b - - 1}{a^{2} - b^{2}}$

Step 1.2.3

Multiply $- 1$ by $- 1$ .

$\frac{3 a - 1 - 3 b + 1}{a^{2} - b^{2}}$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine the opposite terms in $3 a - 1 - 3 b + 1$ .

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Step 1.3.1.1

Add $- 1$ and $1$ .

$\frac{3 a - 3 b + 0}{a^{2} - b^{2}}$

Step 1.3.1.2

Add $3 a - 3 b$ and $0$ .

$\frac{3 a - 3 b}{a^{2} - b^{2}}$

Step 1.3.2

Factor $3$ out of $3 a - 3 b$ .

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Step 1.3.2.1

Factor $3$ out of $3 a$ .

$\frac{3 (a) - 3 b}{a^{2} - b^{2}}$

Step 1.3.2.2

Factor $3$ out of $- 3 b$ .

$\frac{3 (a) + 3 (- b)}{a^{2} - b^{2}}$

Step 1.3.2.3

Factor $3$ out of $3 (a) + 3 (- b)$ .

$\frac{3 (a - b)}{a^{2} - b^{2}}$

Step 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 $b = b$ .

$\frac{3 (a - b)}{(a + b) (a - b)}$

Step 3

Cancel the common factor of $a - b$ .

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Step 3.1

Cancel the common factor.

$\frac{3 (a - b)}{(a + b) (a - b)}$

Step 3.2

Rewrite the expression.

$\frac{3}{a + b}$