Simplify (4x)/(x+3)-(4x^2-7)/(x^2+3x)

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

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

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

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

Factor $x$ out of $3 x$ .

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Apply the distributive property.

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

Multiply $4$ by $- 1$ .

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

Multiply $- 1$ by $- 7$ .

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

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

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

Add $0$ and $7$ .

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