SOLUTION: can you teach me how to do a rational equation and check it? x/6-x/8=1

Question 76648: can you teach me how to do a rational equation and check it?
x/6-x/8=1
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
You can get rid of both denominators by multiplying all the terms on both sides of the equation
by one of two methods. You can either first multiply the entire equation first by 6 and next
by 8 or you can multiply the entire equation by 48, the product of 6*8.
.
Let's do it in two stages. First multiply by 6 to get:
.

.
Then multiply this equation by 8 to get:
.

.
At this point you are at the same place that you would have been if you had just multiplied
the entire equation by 48 ... the product of the denominators.
.
Now, where you have the same term in the denominator and the numerator, you can cancel them
out as follows:
.

.
This leaves you with:
.

.
Notice that I multiplied out the right side. Now you can combine the two terms on the
left side to get:
.

.
and this can be solved by dividing both the left and right side by 2 to get:
.

.
Check this by going back to the original problem:
.

.
Now substitute 24 for x and you get:
.

.
But 24 divided by 6 is 4 and 24 divided by 8 is 3. Substitute these values and the equation
becomes:
.

.
And obviously the left side equals the right side. So our answer of is correct.
.
You can use this method to get rid of the denominators, and then you are working with an
ordinary old algebraic equation ... which is a lot easier than trying to mess around with
fractions. Hope this helps you to understand a method of solving an equation like this
one.
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