You can put this solution on YOUR website! As you described it, the problem you are trying to solve is:
.
.
Get rid of the denominator by multiplying both sides of the equation (all terms) by x and you have:
.
.
Note that the first term on the left side becomes .
.
Also note that in the second term on the left side, you can cancel the multiplier x with the denominator x. After these two actions the equation becomes:
.
.
which simplifies to:
.
.
Get rid of the -6x on the right side by adding +6x to both sides to get:
.
.
This quadratic equation can be factored as shown below:
.
.
Note that this equation will be true if either of the factors is equal to zero. If either factor is equal to zero the left side will have a multiplication by zero and will, therefore, equal the zero on the right side.
.
So we can solve this equation by finding what numbers will make the two factors equal to zero. Do this by setting each factor (one at a time) equal to zero to get:
. which is solved by subtracting 5 from both sides to get x = -5
.
and
. which is solved by subtracting 1 from both sides to get x = -1
.
Your problem has two correct answers. They are x = -5 and x = -1.
.
You can check these answers by returning to the original problem and substituting these values one at a time for x.
.
.
set x = -5 and you have:
. and this simplifies to which is true.
.
Then set x = -1 and you have:
. and this simplifies to which is also true.
.
Both answers are OK because they make the original problem true.
.
Hope this helps you to understand the problem.
.
(