Question

Express as a single fraction in its simplest form
`(3)/(x+2) + (4)/(x-3)`

Answer 1

`(3)/(x + 2) + (4)/(x - 3) = (3(x - 3))/((x + 2)(x - 3)) + (4(x + 2))/((x + 2)(x - 3)) = (3x - 9)/(x^(2) - x - 6) + (4x+ 8)/(x^(2) - x - 6) =(7x -1)/(x^(2) - x - 6)`

Answer 2

`D:x+2\\eq0\to x\\eq-2\ and\ x-3\\eq0\to x\\eq3\\\\(3)/(x+2)+(4)/(x-3)=(3(x-3))/((x+2)(x-3))+(4(x+2))/((x+2)(x-3))=(3(x)+3(-3)+4(x)+4(2))/((x)(x)+(x)(-3)+(2)(x)+2(-3))\\\\=(3x-9+4x+8)/(x^2-3x+2x-6)=\boxed{(7x-1)/(x^2-x-6)}`