Algebra Examples

$\frac{4 x}{x^{2} + 3 x} - \frac{5}{x + 3}$

Step 1

Simplify each term.

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Step 1.1

Factor $x$ out of $x^{2} + 3 x$ .

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Step 1.1.1

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

$\frac{4 x}{x \cdot x + 3 x} - \frac{5}{x + 3}$

Step 1.1.2

Factor $x$ out of $3 x$ .

$\frac{4 x}{x \cdot x + x \cdot 3} - \frac{5}{x + 3}$

Step 1.1.3

Factor $x$ out of $x \cdot x + x \cdot 3$ .

$\frac{4 x}{x (x + 3)} - \frac{5}{x + 3}$

Step 1.2

Cancel the common factor of $x$ .

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Step 1.2.1

Cancel the common factor.

$\frac{4 x}{x (x + 3)} - \frac{5}{x + 3}$

Step 1.2.2

Rewrite the expression.

$\frac{4}{x + 3} - \frac{5}{x + 3}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{4 - 5}{x + 3}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $5$ from $4$ .

$\frac{- 1}{x + 3}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{1}{x + 3}$