You can put this solution on YOUR website! Solving for a variable, like b, always means getting variable by itself on one side of the equation. So our goal is to get an equation like:
b = some expression
Or some expression = b
To start with, let's eliminate the fractions. Fractions can be eliminated in an equation if you multiply both sides of the equation by the Lowest Common Denominator (LCD) of all the denominators (including denominators which are on opposite sides of the equation).
In your equation you have two fractions with denominators of a and b. Since a and b have no common factors the LCD will simply be a*b. So we will multiply both sides of your equation by :
Using the distributive property on the left side we get:
As we simplify this, the a's cancel in the first term and the b's cancel in the second term giving us:
The fractions are now gone. Next we will isolate the b's. Subtract b from both sides to get the terms with b on one side:
Now factor out the b on the right side:
Now we divide both sides by (ac-1) giving:
which, since b is now by itself, is the solution.
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