Algebra Examples

$f (x) = \frac{3}{x + 2} - \sqrt{x - 3}$

Step 1

Rewrite the function as an equation.

$y = \frac{3}{x + 2} - \sqrt{x - 3}$

Step 2

Simplify $\frac{3}{x + 2} - \sqrt{x - 3}$ .

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Step 2.1

To write $- \sqrt{x - 3}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$y = \frac{3}{x + 2} - \sqrt{x - 3} \cdot \frac{x + 2}{x + 2}$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine $- \sqrt{x - 3}$ and $\frac{x + 2}{x + 2}$ .

$y = \frac{3}{x + 2} + \frac{- \sqrt{x - 3} (x + 2)}{x + 2}$

Step 2.2.2

Combine the numerators over the common denominator.

$y = \frac{3 - \sqrt{x - 3} (x + 2)}{x + 2}$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Apply the distributive property.

$y = \frac{3 - \sqrt{x - 3} x - \sqrt{x - 3} \cdot 2}{x + 2}$

Step 2.3.2

Multiply $2$ by $- 1$ .

$y = \frac{3 - \sqrt{x - 3} x - 2 \sqrt{x - 3}}{x + 2}$