Question

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

Solve for x:

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

Answer 1

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

It can be rewritten as:

⇒ `(14 - (x - 3))/(x+3)-5/(x+1)`

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

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

⇒ (11 − x)(x + 1) = 5(x + 3)

⇒ 11x + 11 − x² − x = 5x + 15

⇒ −x² + 10x + 11 = 5x + 15

⇒ −x² + 10x − 5x + 11 − 15 = 0

⇒ −x² + 5x −4 = 0

⇒ x² − 5x + 4 = 0

⇒ x² − 4x − x + 4 = 0

⇒ x(x − 4) −1(x − 4) = 0

⇒ (x − 1)(x − 4) = 0

⇒ x = 1 or x = 4.

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