Solve by Factoring 9+16/(a-2)=(8a)/(a-2)

$9 + \frac{16}{a - 2} = \frac{8 a}{a - 2}$

Step 1

Subtract $\frac{8 a}{a - 2}$ from both sides of the equation.

$9 + \frac{16}{a - 2} - \frac{8 a}{a - 2} = 0$

Step 2

Simplify $9 + \frac{16}{a - 2} - \frac{8 a}{a - 2}$ .

Find the common denominator.

Write $9$ as a fraction with denominator $1$ .

$\frac{9}{1} + \frac{16}{a - 2} - \frac{8 a}{a - 2} = 0$

Multiply $\frac{9}{1}$ by $\frac{a - 2}{a - 2}$ .

$\frac{9}{1} \cdot \frac{a - 2}{a - 2} + \frac{16}{a - 2} - \frac{8 a}{a - 2} = 0$

Multiply $\frac{9}{1}$ by $\frac{a - 2}{a - 2}$ .

$\frac{9 (a - 2)}{a - 2} + \frac{16}{a - 2} - \frac{8 a}{a - 2} = 0$

Combine the numerators over the common denominator.

$\frac{9 (a - 2) + 16 - 8 a}{a - 2} = 0$

Simplify each term.

Apply the distributive property.

$\frac{9 a + 9 \cdot - 2 + 16 - 8 a}{a - 2} = 0$

Multiply $9$ by $- 2$ .

$\frac{9 a - 18 + 16 - 8 a}{a - 2} = 0$

Subtract $8 a$ from $9 a$ .

$\frac{a - 18 + 16}{a - 2} = 0$

Add $- 18$ and $16$ .

$\frac{a - 2}{a - 2} = 0$

Cancel the common factor of $a - 2$ .

Cancel the common factor.

$\frac{a - 2}{a - 2} = 0$

Rewrite the expression.

$1 = 0$

Step 3

Since $1 \neq 0$ , there are no solutions.

No solution