Simplify (7x)/(2x)-(x-2)/(20x+16)

$\frac{7 x}{2 x} - \frac{x - 2}{20 x + 16}$

Step 1

Simplify each term.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{7 x}{2 x} - \frac{x - 2}{20 x + 16}$

Rewrite the expression.

$\frac{7}{2} - \frac{x - 2}{20 x + 16}$

Factor $4$ out of $20 x + 16$ .

Factor $4$ out of $20 x$ .

$\frac{7}{2} - \frac{x - 2}{4 (5 x) + 16}$

Factor $4$ out of $16$ .

$\frac{7}{2} - \frac{x - 2}{4 (5 x) + 4 (4)}$

Factor $4$ out of $4 (5 x) + 4 (4)$ .

$\frac{7}{2} - \frac{x - 2}{4 (5 x + 4)}$

Step 2

To write $\frac{7}{2}$ as a fraction with a common denominator, multiply by $\frac{2 (5 x + 4)}{2 (5 x + 4)}$ .

$\frac{7}{2} \cdot \frac{2 (5 x + 4)}{2 (5 x + 4)} - \frac{x - 2}{4 (5 x + 4)}$

Step 3

Write each expression with a common denominator of $4 (5 x + 4)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{2}$ by $\frac{2 (5 x + 4)}{2 (5 x + 4)}$ .

$\frac{7 (2 (5 x + 4))}{2 (2 (5 x + 4))} - \frac{x - 2}{4 (5 x + 4)}$

Multiply $2$ by $2$ .

$\frac{7 (2 (5 x + 4))}{4 (5 x + 4)} - \frac{x - 2}{4 (5 x + 4)}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 (2 (5 x + 4)) - (x - 2)}{4 (5 x + 4)}$

Step 5

Simplify the numerator.

Multiply $7$ by $2$ .

$\frac{14 (5 x + 4) - (x - 2)}{4 (5 x + 4)}$

Apply the distributive property.

$\frac{14 (5 x) + 14 \cdot 4 - (x - 2)}{4 (5 x + 4)}$

Multiply $5$ by $14$ .

$\frac{70 x + 14 \cdot 4 - (x - 2)}{4 (5 x + 4)}$

Multiply $14$ by $4$ .

$\frac{70 x + 56 - (x - 2)}{4 (5 x + 4)}$

Apply the distributive property.

$\frac{70 x + 56 - x - - 2}{4 (5 x + 4)}$

Multiply $- 1$ by $- 2$ .

$\frac{70 x + 56 - x + 2}{4 (5 x + 4)}$

Subtract $x$ from $70 x$ .

$\frac{69 x + 56 + 2}{4 (5 x + 4)}$

Add $56$ and $2$ .

$\frac{69 x + 58}{4 (5 x + 4)}$