Simplify (2x)/(x+5)-(2x^2-3)/(x^2+5x)

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

Factor $x$ out of $x^{2} + 5 x$ .

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

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

Factor $x$ out of $5 x$ .

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

Factor $x$ out of $x \cdot x + x \cdot 5$ .

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

To write $\frac{2 x}{x + 5}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{2 x}{x + 5} \cdot \frac{x}{x} - \frac{2 x^{2} - 3}{x (x + 5)}$

Write each expression with a common denominator of $(x + 5) x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 x}{x + 5}$ by $\frac{x}{x}$ .

$\frac{2 x \cdot x}{(x + 5) x} - \frac{2 x^{2} - 3}{x (x + 5)}$

Reorder the factors of $(x + 5) x$ .

$\frac{2 x \cdot x}{x (x + 5)} - \frac{2 x^{2} - 3}{x (x + 5)}$

Combine the numerators over the common denominator.

$\frac{2 x \cdot x - (2 x^{2} - 3)}{x (x + 5)}$

Simplify the numerator.

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

Move $x$ .

$\frac{2 (x \cdot x) - (2 x^{2} - 3)}{x (x + 5)}$

Multiply $x$ by $x$ .

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

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $- 3$ .

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

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

$\frac{0 + 3}{x (x + 5)}$

Add $0$ and $3$ .

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