solve for x

Question

how do i salove this problems

x/(x-3) -(x+3)/x =1/x solve for x.

Answer 1

     x/(x - 3) - (x + 3)/x = 1/x

When fractions are added/subtracted from one another, they need to have a common denominator. Since the second term on the left hand side of the equation and the term on the right hand side of the equation share a common denominator, that being 'x', we can combine these fractions. So first add the second term on the left hand side of the equation to both sides of the equation. That is,

     x/(x - 3) - (x + 3)/x + (x + 3)/x = 1/x + (x + 3)/x

     x/(x - 3) = (1 + (x + 3))/x = (x + 1 + 3)/x

     x/(x - 3) = (x + 4)/x

Next, cross multiply:

     x·x = (x - 3)·(x + 4)

     x² = x·x + x·4 - 3·x - 3·4 = x² + 4x - 3x - 12

     x² = x² + x - 12

To solve for x, set the equation equal to 0 by first subtracting 'x²' from both sides of the equation then adding 12 to both sides of the equation:

     x² - x² = x² + x - 12 - x² 

     0 = x - 12

     0 + 12 = x - 12 + 12

     12 = x     ==>     x = 12