Simplify (a-4)/(4a-8)+1/(2a-4)

$\frac{a - 4}{4 a - 8} + \frac{1}{2 a - 4}$

Step 1

Simplify each term.

Factor $4$ out of $4 a - 8$ .

Factor $4$ out of $4 a$ .

$\frac{a - 4}{4 (a) - 8} + \frac{1}{2 a - 4}$

Factor $4$ out of $- 8$ .

$\frac{a - 4}{4 a + 4 \cdot - 2} + \frac{1}{2 a - 4}$

Factor $4$ out of $4 a + 4 \cdot - 2$ .

$\frac{a - 4}{4 (a - 2)} + \frac{1}{2 a - 4}$

Factor $2$ out of $2 a - 4$ .

Factor $2$ out of $2 a$ .

$\frac{a - 4}{4 (a - 2)} + \frac{1}{2 (a) - 4}$

Factor $2$ out of $- 4$ .

$\frac{a - 4}{4 (a - 2)} + \frac{1}{2 a + 2 \cdot - 2}$

Factor $2$ out of $2 a + 2 \cdot - 2$ .

$\frac{a - 4}{4 (a - 2)} + \frac{1}{2 (a - 2)}$

Step 2

To write $\frac{1}{2 (a - 2)}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{a - 4}{4 (a - 2)} + \frac{1}{2 (a - 2)} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $4 (a - 2)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2 (a - 2)}$ by $\frac{2}{2}$ .

$\frac{a - 4}{4 (a - 2)} + \frac{2}{2 (a - 2) \cdot 2}$

Multiply $2$ by $2$ .

$\frac{a - 4}{4 (a - 2)} + \frac{2}{4 (a - 2)}$

Step 4

Combine the numerators over the common denominator.

$\frac{a - 4 + 2}{4 (a - 2)}$

Step 5

Add $- 4$ and $2$ .

$\frac{a - 2}{4 (a - 2)}$

Step 6

Cancel the common factor of $a - 2$ .

Cancel the common factor.

$\frac{a - 2}{4 (a - 2)}$

Rewrite the expression.

$\frac{1}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$