# How do you solve #(x-2)/(x^2-7x+10)=1/(5x-10)-1/(x-5)#?

##### 3 Answers

Simplify by getting everything on the same common denominator and then rearrange to find x

#### Explanation:

You can simplify the left side.

#### Explanation:

Obtaining the roots for

Then

In the expression:

#### Explanation:

Factor each denominator.

#(x-2)/((x-5)(x-2))=1/(5(x-2))-1/(x-5)#

Simplify the first fraction by dividing

#1/(x-5)=1/(5(x-2))-1/(x-5)#

Add

#2/(x-5)=1/(5(x-2)#

Cross multiply.

#10(x-2)=x-5#

Simplify and solve.

#10x-20=x-5#

#9x-20=-5#

#9x=15#

#x=15/9#

#x=5/3#

When solving rational equations such as these, it's always a good idea to go back and check that this answer isn't an invalid answer. Invalidity would occur if