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

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#### Solution

`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= x^{2}+4x+3

⇒x^{2}−5x+4 = 0

⇒x^{2}−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.

Concept: Solutions of Quadratic Equations by Factorization

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