Math Is Fun Forum

mykel

Member

Registered: 2007-02-11

Posts: 4

finding X in fraction

I have the following problem.

1/x-3 + 2/x-5 = 3/x^2 - 8x + 15

I know the answer is x = 14/3, but what's the procedure for that conclusion?

Thanks!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: finding X in fraction

In problems like this, you generally need to multiply everything by the all of the denominators to get rid of them.

You have: 1/(x-3) + 2/(x-5) = 3/(x² - 8x + 15)
Factorise the right-hand denominator: 1/(x-3) + 2/(x-5) = 3/(x-3)(x-5)
Multiply by (x-3)(x-5): (x-5) + 2(x-3) = 3
Expand: x-5 + 2x - 6 = 3
Simplify: 3x = 14
Solve: x = 14/3.

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Why did the vector cross the road?
It wanted to be normal.

fasf

Guest

Re: finding X in fraction

dude..its so easy

kylekatarn

Member

Registered: 2005-07-24

Posts: 445

Re: finding X in fraction

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Last edited by kylekatarn (2020-01-03 11:19:28)