Simplify (2x-12)/(8x-12)+(16x-15)/(8x-12)

$\frac{2 x - 12}{8 x - 12} + \frac{16 x - 15}{8 x - 12}$

Step 1

Combine the numerators over the common denominator.

$\frac{2 x - 12 + 16 x - 15}{8 x - 12}$

Step 2

Add $2 x$ and $16 x$ .

$\frac{18 x - 12 - 15}{8 x - 12}$

Step 3

Subtract $15$ from $- 12$ .

$\frac{18 x - 27}{8 x - 12}$

Step 4

Factor $9$ out of $18 x - 27$ .

Factor $9$ out of $18 x$ .

$\frac{9 (2 x) - 27}{8 x - 12}$

Factor $9$ out of $- 27$ .

$\frac{9 (2 x) + 9 (- 3)}{8 x - 12}$

Factor $9$ out of $9 (2 x) + 9 (- 3)$ .

$\frac{9 (2 x - 3)}{8 x - 12}$

Step 5

Factor $4$ out of $8 x - 12$ .

Factor $4$ out of $8 x$ .

$\frac{9 (2 x - 3)}{4 (2 x) - 12}$

Factor $4$ out of $- 12$ .

$\frac{9 (2 x - 3)}{4 (2 x) + 4 (- 3)}$

Factor $4$ out of $4 (2 x) + 4 (- 3)$ .

$\frac{9 (2 x - 3)}{4 (2 x - 3)}$

Step 6

Cancel the common factor of $2 x - 3$ .

Cancel the common factor.

$\frac{9 (2 x - 3)}{4 (2 x - 3)}$

Rewrite the expression.

$\frac{9}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$