SOLUTION: solve for x 4/x-2+3/x+2=5x/x^2-4

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Question 273678: solve for x
4/x-2+3/x+2=5x/x^2-4
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

Solving an equation without fractions is usually easier than solving one with fractions. So we'll start by eliminating the fractions. To eliminate fractions from an equation:
  1. Simplify each side
  2. Multiply both sides of the equation by the Lowest Common Denominator (LCD)

Both sides of your equation are already simplified so we can go straight to finding the LCD. The LCD is easier to see if you factor the denominators:

The LCD, as I hope you see, is (x+2)(x-2). So this is what we will multiply both sides by this:

On the left side we need to use the Distributive Property to multiply:

Before we multiply all this, let's cancel common factors between the numerators and the denominators:

which simplifies to:

or

Multiplying we get:

Simplifying we get:

This is a fairly simple equation to solve. Subtract 7x from each side:

Divide both sides by -2:


Back at the start we multiplied both sides of the equation by the LCD. The LCD, (x+2)(x-2), could be zero depending on the value of x. Whenever you multiply both sides of an equation by an expression that might be zero, it is important, not just a good idea, to check our answers. This is so because when we multiply by something that might be zero we may be introducing "solutions" which don't actually fit the equation.
When checking answers, always use the original equation:

Checking x = -1:

which simplifies as follows:



Check!
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