How do you simplify (x+3)/(x+5) + 6/(x^2+3x-10)x+3x+5+6x2+3x−10?

1 Answer
evant939012
Apr 9, 2018

(x(x+1))/((x+5)(x-2))x(x+1)(x+5)(x−2)

Explanation:

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

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

Obtain a common denominator:
(x+3)/(x+5)*(x-2)/(x-2)x+3x+5⋅x−2x−2 --> ((x+3)(x-2))/((x+5)(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+3)(x−2)(x+5)(x−2)
(6+x^2+x-6)/((x+5)(x-2))6+x2+x−6(x+5)(x−2)

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

And that is it. Make sure you state that x cannot be -5−5 or 22, since that would result in division by zero.

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