Simplify (3x)/(x+1)-5/x

$\frac{3 x}{x + 1} - \frac{5}{x}$

To write $\frac{3 x}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{3 x}{x + 1} \cdot \frac{x}{x} - \frac{5}{x}$

To write $- \frac{5}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

$\frac{3 x}{x + 1} \cdot \frac{x}{x} - \frac{5}{x} \cdot \frac{x + 1}{x + 1}$

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

Multiply $\frac{3 x}{x + 1}$ by $\frac{x}{x}$ .

$\frac{3 x \cdot x}{(x + 1) x} - \frac{5}{x} \cdot \frac{x + 1}{x + 1}$

Multiply $\frac{5}{x}$ by $\frac{x + 1}{x + 1}$ .

$\frac{3 x \cdot x}{(x + 1) x} - \frac{5 (x + 1)}{x (x + 1)}$

Reorder the factors of $(x + 1) x$ .

$\frac{3 x \cdot x}{x (x + 1)} - \frac{5 (x + 1)}{x (x + 1)}$

Combine the numerators over the common denominator.

$\frac{3 x \cdot x - 5 (x + 1)}{x (x + 1)}$

Simplify the numerator.

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

Move $x$ .

$\frac{3 (x \cdot x) - 5 (x + 1)}{x (x + 1)}$

Multiply $x$ by $x$ .

$\frac{3 x^{2} - 5 (x + 1)}{x (x + 1)}$

Apply the distributive property.

$\frac{3 x^{2} - 5 x - 5 \cdot 1}{x (x + 1)}$

Multiply $- 5$ by $1$ .

$\frac{3 x^{2} - 5 x - 5}{x (x + 1)}$