You can put this solution on YOUR website! Often the easiest way to solve equations with fractions in them is to start by eliminating the fractions. This can be done by multiplying both sides of the equation by the Lowest Common Denominator (LCD) of all the denominators (even if they are on opposite sides of the equation.
With your equation the two denominators are (x+3) and x. Since there are no common factors between them, the LCD will simply be the product of the two: (x+3)*x. So we will multiply both sides of the equation by (x+3)*x:
Using the distributive property on the left we get:
As we simplify this we find that in the first fraction the (x+3)'s cancel and in the second fraction x's cancel. We end up with:
This is a quadratic equation so we gather everything to one side (by subtracting 5x and 3 from both sides:
Now we factor the trinomial:
In order for any product to be zero, one of the factors must be zero. In other "words": or
Solving each of these separately we get or
These are the two solutions to your equation. (Check them by substituting these values, one at a time, into your equation to see if they work.)
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