Question

How do you simplify `(x+3)/(x+5) + 6/(x^2+3x-10)`?

Answer 1

`(x(x+1))/((x+5)(x-2))`

Explanation:

The quadratic can be factored to `(x+5)(x-2)`.

So the expression is:
`(x+3)/(x+5)+6/((x-2)(x+5))`

Obtain a common denominator:
`(x+3)/(x+5)*(x-2)/(x-2)` --> `((x+3)(x-2))/((x+5)(x-2))`

So the expression is now:
`(6+(x+3)(x-2))/((x+5)(x-2))`
`(6+x^2+x-6)/((x+5)(x-2))`

Sixes cancel, top factor out an x:
`(x(x+1))/((x+5)(x-2))`

And that is it. Make sure you state that x cannot be `-5` or `2`, since that would result in division by zero.