# How do you solve (x - 5) / (x - 8) = (x + 1) / (x - 5)?

Jun 14, 2017

$x = 11$

#### Explanation:

Multiply both sides by $\left(x - 5\right) \left(x - 8\right)$. This will allow you to cancel common factors and get rid of the denominators.

$\frac{\left(x - 5\right) \left(x - 5\right) \cancel{x - 8}}{\cancel{x - 8}} = \frac{\left(x + 1\right) \cancel{x - 5} \left(x - 8\right)}{\cancel{x - 5}}$

${\left(x - 5\right)}^{2} = \left(x + 1\right) \left(x - 8\right)$

Next, multiply out all the brackets:

${x}^{2} - 10 x + 25 = {x}^{2} - 7 x - 8$

Bring all the x-terms to one side and the constants to the other:

${x}^{2} - {x}^{2} - 10 x + 7 x = - 8 - 25$

Simplify and solve for x:

$- 3 x = - 33$

$x = \frac{- 33}{-} 3 = 11$

Jun 14, 2017

x =11 multiply both sides by the denominators to eliminate the fractions then solve for x

#### Explanation:

$\frac{\left(x - 8\right) \times \left(x - 5\right) \times \left(x - 5\right)}{x - 5} = \frac{\left(x - 8\right) \times \left(x - 5\right) \times \left(x + 1\right)}{x - 8}$

Dividing out the denominators gives

$\left(x - 5\right) \times \left(x - 5\right) = \left(x - 8\right) \times \left(x + 1\right)$ Use the distributive property

${x}^{2} - 10 x + 25 = {x}^{2} - 7 x - 8$ subtract x^2 from both sides gives

${x}^{2} - {x}^{2} - 10 x + 25 = {x}^{2} - {x}^{2} - 7 x - 8$ so

$- 10 x + 25 = - 7 x - 8$ add +10x and 8 to both sides

$- 10 x + 10 x + 25 + 8 = - 7 x + 10 x - 8 + 8$ this gives

$33 = 3 x$ divide both sides by 3

$\frac{33}{3} = \frac{3 x}{3}$ so

# 11 = x