SOLUTION: my last question in this section and I can't get it right. I hope you can help me. i am adding RE's with different denominators. here is the problem: 5/x^2-15x+50 +9/x^2-x-20

Question 972494: my last question in this section and I can't get it right. I hope you can help me.
i am adding RE's with different denominators. here is the problem:
5/x^2-15x+50 +9/x^2-x-20
I went ahead and simplified the first equation to look like this: 5/(x-10)(x-5)
the second looks like this: 9/(x-5)(x+4)
now here is where I get stuck. Where do I go from here? I tried to cross multiply using (x-10) and (x+4)
I came up with 5x+20+9x-90/(x-10)(x-5)(x+4) which would give me the answer:
14x-70/(x-10)(x-5)(x+4) but the answer key shows the answer as 14/(x-10)(x+4)
what step am I missing?
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I came up with 5x+20+9x-90/(x-10)(x-5)(x+4) which would give me the answer:
14x-70/(x-10)(x-5)(x+4) but the answer key shows the answer as 14/(x-10)(x+4)
what step am I missing?
-------------
14x-70/(x-10)(x-5)(x+4)
= 14(x-5)/(x-10)(x-5)(x+4)
Cancel (x-5)
= 14/(x-10)(x+4)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your expression is:

5 divided by (x^2 - 15x + 50)
plus
9 divided by (x^2 - x - 20)

you can factor x^2 - 15x + 50 to get (x-5) * (x-10)

you can factor x^2 - x - 20 to get (x-5) * (x-4)

your expression becomes:

5 divided by (x-5) * (x-10)
plus
9 divided by (x-5) * (x-4)

your common denominator will be (x-5) * (x-10) * (x-4)

you will multiply 5 divided by (x-5) * (x-10) by (x-4) / (x-4)

you will multiply 9 divided by (x-5) * (x-4) by (x-10) / (x-10)

you will get:

5 * (x-5) divided by (x-4) * (x-5) * (x-10)
plus
9 * (x-10) divided by (x-4) * (x-5) * (x-10)

you put both fractions under the common denominator and you will get:

5 * (x-5) + 9 * (x-10) divided by (x-4) * (x-5) * (x-10)

you would then simplify the numerator to get:

5x - 25 + 9x - 90 divided by (x-4) * (x-5) * (x-10)

you would then simplify further to get:

(14x - 115) divided by (x-4) * (x-5) * (x-10)

i believe that's as far as you need to go with the simplification.

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