Question

Solve the equation:`14/(x+3)-1=5/(x+1); xne-3,-1` , for x

Answer 1

`14/(x+3)-1=5/(x+1); xne-3,-1`

It can be rewritten as:

`14/(x+3)-5/(x+1)=1`

`(14(x+1)-5(x+3))/((x+1)(x+3))=1`

`(14x+14-5x-15)/(x^2+4x+3)=1`

`(9x-1)/(x^2+4x+3)=1`

On cross multiplying, we get:

9x−1= x²+4x+3

⇒x²−5x+4 = 0
⇒x²−4x−x+4 = 0
⇒x(x−4)− (x−4)=0
⇒(x−1) (x−4)=0
⇒x=1, 4

Thus, the solution of the given equation is 1 or 4.