Algebra Examples

$\frac{4 x}{x + 3} - \frac{4 x^{2} - 7}{x^{2} + 3 x}$

Step 1

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

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Step 1.1

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

$\frac{4 x}{x + 3} - \frac{4 x^{2} - 7}{x \cdot x + 3 x}$

Step 1.2

Factor $x$ out of $3 x$ .

$\frac{4 x}{x + 3} - \frac{4 x^{2} - 7}{x \cdot x + x \cdot 3}$

Step 1.3

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

$\frac{4 x}{x + 3} - \frac{4 x^{2} - 7}{x (x + 3)}$

Step 2

To write $\frac{4 x}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{4 x}{x + 3} \cdot \frac{x}{x} - \frac{4 x^{2} - 7}{x (x + 3)}$

Step 3

Write each expression with a common denominator of $(x + 3) x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4 x}{x + 3}$ by $\frac{x}{x}$ .

$\frac{4 x \cdot x}{(x + 3) x} - \frac{4 x^{2} - 7}{x (x + 3)}$

Step 3.2

Reorder the factors of $(x + 3) x$ .

$\frac{4 x \cdot x}{x (x + 3)} - \frac{4 x^{2} - 7}{x (x + 3)}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 x \cdot x - (4 x^{2} - 7)}{x (x + 3)}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $x$ by $x$ by adding the exponents.

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Step 5.1.1

Move $x$ .

$\frac{4 (x \cdot x) - (4 x^{2} - 7)}{x (x + 3)}$

Step 5.1.2

Multiply $x$ by $x$ .

$\frac{4 x^{2} - (4 x^{2} - 7)}{x (x + 3)}$

Step 5.2

Apply the distributive property.

$\frac{4 x^{2} - (4 x^{2}) - - 7}{x (x + 3)}$

Step 5.3

Multiply $4$ by $- 1$ .

$\frac{4 x^{2} - 4 x^{2} - - 7}{x (x + 3)}$

Step 5.4

Multiply $- 1$ by $- 7$ .

$\frac{4 x^{2} - 4 x^{2} + 7}{x (x + 3)}$

Step 5.5

Subtract $4 x^{2}$ from $4 x^{2}$ .

$\frac{0 + 7}{x (x + 3)}$

Step 5.6

Add $0$ and $7$ .

$\frac{7}{x (x + 3)}$