Question

Solve the equation, using any method. Be sure to check for extraneous solutions.

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

Answer 1

Answer: No real solution.

Explanation:

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

First solve
`x^2+5x+6`

`(2)/((2x+6))-(2)/((x+3)(x+2))=(3)/((x+3))`

`([2(x+3)(x+2)]-[2(2x+6)])/((2x+6)(x+3)(x+2)) = (3)/((x+3))`

`([(2x+6)(x+2)]-(4x-12))/((2x+6)(x+3)(x+2)) = (3)/((x+3))`

`((2x^2+4x+6x+12)-(4x-12))/((2x+6)(x+3)(x+2)) = (3)/((x+3))`

`(2x^2+10x+12-4x+12)/((2x+6)(x+3)(x+2)) = (3)/((x+3))`

`(2x^2+6x+24)/((2x+6)(x+3)(x+2)) = (3)/((x+3))`

Past this point, we can't solve
`2x^2+6x+24` and obtain real values of x. Therefore, there are no real solutions.