2 over x+9 + 5 over x-9?

Question

2 over x+9 + 5 over x-9 add( over is the fraction bar)

Answer 1

7x+27 over (x+9)(x-9)

Answer 2

In this problem you first have to find the least common denominator (LCD), in this case it would be the multiplication of both denominators. Hence our LCD=(x=9)(x-9)

So the first fraction needs to be multiplied by (x-9) both top and bottom which wold give us:
2(x-9)/( (x+9)(x-9))= (2x-18)/((x+9)(x-9))


Now the second fraction needs to be multiplied by (x+9) both top and bottom which would give us:
5(x+9)/((x+9)(x-9))= (5x+45)/((x+9)(x-9))

So now that we have the same LCD=(x+9)(x-9)
then we can just add the numerators of the fractions. Hence
(2x-18)/((x+9)(x-9)) + (5x +45)/((x+9)(x-9)) = (2x-18 + 5x +45)/((x+9)(x-9))= (7x+27)/((x+9)(x-9))

Hope this helps!

Answer 3

(2/(x + 9)) + (5/(x - 9))
Multiply everything by (x + 9)(x - 9)
(2(x - 9) + 5(x + 9))/((x + 9)(x - 9))
(2x - 18 + 5x + 45)/((x + 9)(x - 9))
(7x + 27)/((x + 9)(x - 9))
(7x + 27)/(x^2 - 81)

If that had been (-2/(x + 9)), then i could reduce it.