Simplify (2x+3)/x-1/(x+7)

$\frac{2 x + 3}{x} - \frac{1}{x + 7}$

Step 1

To write $\frac{2 x + 3}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 7}{x + 7}$ .

$\frac{2 x + 3}{x} \cdot \frac{x + 7}{x + 7} - \frac{1}{x + 7}$

Step 2

To write $- \frac{1}{x + 7}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{2 x + 3}{x} \cdot \frac{x + 7}{x + 7} - \frac{1}{x + 7} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $x (x + 7)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 x + 3}{x}$ by $\frac{x + 7}{x + 7}$ .

$\frac{(2 x + 3) (x + 7)}{x (x + 7)} - \frac{1}{x + 7} \cdot \frac{x}{x}$

Multiply $\frac{1}{x + 7}$ by $\frac{x}{x}$ .

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

Reorder the factors of $(x + 7) x$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Expand $(2 x + 3) (x + 7)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $7$ by $2$ .

$\frac{2 x^{2} + 14 x + 3 x + 3 \cdot 7 - x}{x (x + 7)}$

Multiply $3$ by $7$ .

$\frac{2 x^{2} + 14 x + 3 x + 21 - x}{x (x + 7)}$

Add $14 x$ and $3 x$ .

$\frac{2 x^{2} + 17 x + 21 - x}{x (x + 7)}$

Subtract $x$ from $17 x$ .

$\frac{2 x^{2} + 16 x + 21}{x (x + 7)}$