# How do you solve (x - 3) / (x - 4) = (x - 5 )/( x + 4)?

Jun 5, 2018

$x = \frac{16}{5}$

#### Explanation:

Given:

$\frac{x - 3}{x - 4} = \frac{x - 5}{x + 4}$

Multiply both sides by $\left(x - 4\right) \left(x + 4\right)$ to get:

$\left(x - 3\right) \left(x + 4\right) = \left(x - 5\right) \left(x - 4\right)$

Multiplying out, this becomes:

${x}^{2} + x - 12 = {x}^{2} - 9 x + 20$

Adding $- {x}^{2} + 9 x + 12$ to both sides, this becomes:

$10 x = 32$

Dividing both sides by $10$, we find:

$x = \frac{32}{10} = \frac{16}{5}$

Note that this value of $x$ results in non-zero values of $\left(x - 4\right)$ and $\left(x + 4\right)$ so is a valid solution of the given rational equation.