How do you solve 5-2/(x-6) = (10-2x)/(x-6)52x6=102xx6?

1 Answer
May 29, 2017

no solution

Explanation:

Let's give everything the same denominator. Fortunately, two of the three components already share the same denominator (x-6)(x6).

If we multiply 55 by (x-6)/(x-6)x6x6, all the components will be "combinable":

(5x-30)/(x-6) - 2/(x-6) = (10-2x)/(x-6)5x30x62x6=102xx6

Combine like-terms

((5x-30)-(2))/(x-6) = (10-2x)/(x-6)(5x30)(2)x6=102xx6

Multiply by (x-6x6) on both sides

5x-30-2 = 10-2x5x302=102x

Simplify

5x-32=10-2x5x32=102x

Add 2x to both sides

7x-32=107x32=10

Add 3232 to both sides

7x=427x=42

Divide by 77 on both sides

x=6x=6

Just to check our work, let's solve the equation, replacing xx with 66:

5- 2/(6-6) = (10-2xx6)/(6-6)5266=102×666

5-2/0=(-2)/0520=20

Uh oh! We're dividing by ZERO! that's illegal, so there are no solutions.