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

2 Answers
Jun 14, 2017

x=11

Explanation:

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

((x-5)(x-5)cancel(x-8))/cancel(x-8)=((x+1)cancel(x-5)(x-8))/cancel(x-5)

(x-5)^2=(x+1)(x-8)

Next, multiply out all the brackets:

x^2-10x+25=x^2-7x-8

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

x^2-x^2-10x+7x=-8-25

Simplify and solve for x:

-3x=-33

x=(-33)/-3=11

Jun 14, 2017

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

Explanation:

{ ( x-8) xx(x-5) xx (x-5)}/(x-5) = {(x-8) xx (x-5) xx ( x+1)}/(x-8)

Dividing out the denominators gives

(x -5)xx(x-5) = (x-8) xx ( x+1) Use the distributive property

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

x^2 - x^2 -10x + 25 = x^2 - x^2 -7x -8 so

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

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

33 = 3x divide both sides by 3

33/3 =( 3x)/3 so

# 11 = x