Algebra Examples

$\frac{5 x + 1}{x^{2} - 64} - \frac{4 x - 7}{x^{2} - 64}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{5 x + 1 - (4 x - 7)}{x^{2} - 64}$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$\frac{5 x + 1 - (4 x) - - 7}{x^{2} - 64}$

Step 1.2.2

Multiply $4$ by $- 1$ .

$\frac{5 x + 1 - 4 x - - 7}{x^{2} - 64}$

Step 1.2.3

Multiply $- 1$ by $- 7$ .

$\frac{5 x + 1 - 4 x + 7}{x^{2} - 64}$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $4 x$ from $5 x$ .

$\frac{x + 1 + 7}{x^{2} - 64}$

Step 1.3.2

Add $1$ and $7$ .

$\frac{x + 8}{x^{2} - 64}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $64$ as $8^{2}$ .

$\frac{x + 8}{x^{2} - 8^{2}}$

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 $a = x$ and $b = 8$ .

$\frac{x + 8}{(x + 8) (x - 8)}$

Step 3

Cancel the common factor of $x + 8$ .

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Step 3.1

Cancel the common factor.

$\frac{x + 8}{(x + 8) (x - 8)}$

Step 3.2

Rewrite the expression.

$\frac{1}{x - 8}$