# How do you solve #1/(r-2)+1/(r^2-7r+10)=6/(r-2)# and check for extraneous solutions?

##### 1 Answer

Oct 29, 2016

#### Answer:

#### Explanation:

Note that

So the given equation can be written:

#1/(r-2)+1/((r-2)(r-5)) = 6/(r-2)#

Multiply through by

#1+1/(r-5)=6#

(noting that

Subtract

#1/(r-5) = 5#

Take the reciprocal of both sides to get:

#r-5 = 1/5#

Add

#r = 26/5#

Since