You can put this solution on YOUR website!
There are different ways to solve this. The way I like to to start by eliminating the fractions. To eliminate the fractions we will need the Lowest Common Denominator (LCD). And to find the LCD we need to know the factors of the denominators. So we start by factoring the denominators:
Now we can see that the LCD is (x+4)(x-4). Next we multiply each side of the equation by the LCD:
On the left side we will need to use the Distributive Property:
Now all the fractions disappear!
leaving:
which simplifies as follows:
x - 4 + x + 4 = 1
2x = 1
This is an extremely simple equation to solve. Just divide both sides by 2:
When solving equations where the variable is in one or more denominators, you should check to make sure the your "solution(s)" do not make any denominators zero. A quick check of the original equation should show that when x = 1/2, none of the three denominators will be zero. (If there had been a zero denominator, we would have to reject x = 1/2 and, since this was the only solution we found, your equation would then have no solution!)
You are welcome to complete the check to see if we made any mistakes.
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