Question

How do you solve `(2x)/(x-3)=(3x)/(x^2-9)+2`?

Answer 1

`x=-6`

Explanation:

`(2x)/(x-3)=(3x)/(x^2-9)+2`
`=>(2x)/(x-3)=(3x)/((x-3)(x+3))+2/1`
`=>((2x)(x+3))/((x-3)(x+3))=(3x(1))/((x-3)(x+3))+(2(x-3)(x+3))/((x-3)(x+3)`
`=>2x(x+3)=3x+2(x^2-9)`
`=>cancel(2x^2)+6x=3x+cancel(2x^2)-18`
`=>6x=3x-18`
`=>3x=-18=>x=-6`