Question

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

Answer 1

`(x^2+3x+3)/((x-3)(x+3))`

Explanation:

`"before adding the fractions we require them to have"`
`"a "color(blue)"common denominator"`

`"factorise the denominator "x^2-9`

`x^2-9=(x-3)(x+3)larrcolor(blue)"difference of squares"`

`"multiply numerator/denominator of"x/(x-3)" by "(x+3)`

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

`"add the numerators leaving the denominator"`

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