Solve for x

Question

Solve for x:

 

2/(x-2) = (x+2)/x

Answer 1

Georgina,

 

If we cross multiply, we get:

 

2x = (x - 2)(x + 2)

 

2x = x² - 4

 

0 = x² - 2x - 4

 

You can use a number of methods to factor this quadratic to find its roots.

 

The quadratic formula comes to mind.

 

I'll leave the rest to you.

 

 

 

 

Answer 2

2 / (x - 2) = (x + 2) / x

 

Multiply both sides by x(x - 2)

 

2x = (x - 2)(x + 2) = x² - 4

 

x² - 2x - 4 = 0

 

Solve for x using the quadratic formula.

 

x = {2 ± √[(-2)² - 4(-4)]} / 2 = (2 ± √20) / 2

 

x = (2 ± 2√5) / 2 = 1 ± √5 

 

x = 1 ± √5

Answer 3

2/(x-2) = (x+2)/x

 

Cross Multiply

 

2(x) = (x-2)(x+2)

  2x = x² - 4

  0 = x² - 2x - 4

 

This will not factor, but you can use the quadratic formula, or completing the square to solve for x.  I used completing the square.

 

   x² - 2x = 4 

   

   NOTE:  b = -2 .... we take 1/2 of b, square that, and add to both sides

                              (-2/2)² = (-1)² = 1

 

   x² - 2x + 1 = 4 + 1

   (x - 1)(x - 1) = 5        ... factor

   (x - 1)² = 5

   (x - 1)±√5                 ... take square root of both sides

    x - 1 = √5    or  x - 1 = -√5

         x = 1 + √5    or x = 1 - √5