Question

For the rational equation, x^2+5x+6/x+3=3 , what is a valid value of x?.

Answer 1

The answer for this question is 1

Answer 2

x= -3 and x = 1 are the values.

Explanation:

For the rational equation given we have to find the value of x.

`(x^(2)+5x+6)/((x+3))=3`

By cross multiplication

`x^(2)+5x+6=3(x+3)`

We factorize left hand side (L.H.S.) of the equation first.

`x^(2)+5x+6=x^(2)+3x+2x+6`

=
`x(x+3)+2(x+3)`

=
`(x+2)(x+3)`

Now factorized form of the eqation is

`(x+2)(x+3)=3(x+3)`

`(x+2)(x+3)-3(x+3)=0`

`(x+3)(x-1)=0`

x+3= 0 ⇒ x = -3

x - 1 = 0 ⇒ x = 1

Therefore, x= -3 and x = 1 are the values.