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2x-3/x+1 = 2 - 3x-1/x+1

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2 Answers

Arlandria, you have to use parentheses for this kind of problem, or use the bar notation to avoid the double reading!!
(2x - 3) / (x + 1) = 2 - (3x - 1) / (x + 1)
or
  2x – 3                 3x – 1
————  =  2  –  ————
   x + 1                  x + 1

  2x – 3            3x – 1
—————  +  ————  =  2
   x + 1             x + 1

   2x – 3 + 3x – 1
—————————  =  2
          x + 1

  5x – 4
 ————  =  2  
   x + 1

5x – 4 = 2(x + 1)
5x – 4 = 2x + 2
5x – 2x = 4 + 2
3x = 6
 x = 2

Comments

Just one question: how did you figure out it is (2x-3)/(x+1), not 2x-3/(x+1), for example??

A+ question, Kiril. He-he, because I did tons of virtual problems with students and know formats of the problems.

... plus logic! Student used spaces! :)

 

First, I assume that -3/x+1 means that -3 is divided by x and then 1 is added to the result. And the same is true for the right-hand side.

First, collect like terms. Let us move every single term to the left so that right side equals to zero.

2x-3/x+1=2-3x-1/x+1  =>  2x-3/x+1-2+3x+1/x-1=0 

Now collect like terms. We obtain:

5x-2/x-2=0 Now let us have common denominator in the expression on the left side.

(5x2-2-2x)/x=0

This is true only is 5x2-2x-2=0; Solutions to this equation are given by:

x1,2=[2±√(4-4*5*(-2))]/10; After simple calculations, we obtain:

x1=(1-√11)/5; x2=(1+√11)/5;