For the rational equation,(x^(2)+5x+6)/(x+3)=1 , what is a valid value of x?

Question

For the rational equation,
`(x^(2)+5x+6)/(x+3)=1` , what is a valid value of x?

Answer 1

-3 or -1 is a valid value for x

Explanation:

We start by cross multiplying;

So the expression becomes;

x^2 + 5x + 6 = 1(x + 3)

x^2 + 5x + 6 = x + 3

x^2 + 5x -x + 6-3 = 0

x^2 + 4x + 3 = 0

x^2 + x + 3x + 3 = 0

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

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

x + 3 = 0 or x + 1 = 0

x = -3 or x = -1