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

Re: Solving Rational functions

Quote:

Originally Posted by

**skg94** 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

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

**Determine the domain of the equation.**

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

$\displaystyle 6x + 3x(x-3)=2x^2 - 5(x-3)$

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

$\displaystyle x^2+2x-15=0$

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