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Math Help - Solving Rational functions

  1. #1
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    Solving Rational functions

    Can someone explain this to me?

    1. 2+ 5/x+3 = 1 - (x+1) /x
    2. 6x/(x-3) +3x = 2x^2/(x-3) -5

    how do i solve this multiple by x? i dont understand, i know i just asked but im very confused at how to solve these types of questions. How to isolate x to oneside and get ride of the denominator
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  2. #2
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    Re: Solving Rational functions

    Quote Originally Posted by skg94 View Post
    Can someone explain this to me?

    1. 2+ 5/x+3 = 1 - (x+1) /x
    2. 6x/(x-3) +3x = 2x^2/(x-3) -5

    how do i solve this multiple by x? i dont understand, i know i just asked but im very confused at how to solve these types of questions. How to isolate x to oneside and get ride of the denominator
    1. The 1st equation is incomplete.

    2. I assume that you want to solve

    \frac{6x}{x-3} + 3x = \frac{2x^2}{x-3} - 5

    Determine the domain of the equation.

    Multiply through by (x - 3). You'll get:

    6x + 3x(x-3)=2x^2 - 5(x-3)

    Expand the brackets, collect like terms at LHS of the equation. You should come out with:

    x^2+2x-15=0

    Apply the quadratic formula. You'll get 2 solutions. Check your solutions against the domain. The finmal result should be x = -5.
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