SOLUTION: Divide and Simplify (2y-6/121)/(y-3/22)

Question 421673: Divide and Simplify
(2y-6/121)/(y-3/22)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

This is a fraction divided by a fraction. When you first learned about division with fractions, back when it was just 2/3 divided by 6/7, you learned to change it into multiplying by the reciprocal. That's still true, even though there are now variables in the fractions. Changing your expression into multiplying by the reciprocal we get:

And when you learned about multiplying fractions, you should have been told it was OK to cancel factors that are common to both the numerator and denominator, even from one fraction across to the other. This was optional but it made the multiplication easier. As the fractions get more and more complicated, the advantages to canceling before you multiply get greater and greater. So we are going to cancel factors before we multiply. And of course to cancel factors we must know what the factors are. So the next step is to factor. (If you don't factor now, you will have to factor later when you try to reduce your answer. The factoring is easier now than later, too.) Factoring we get:

We can see several factors that will cancel:

leaving:

This, you must agree, is much easier to multiply than what we had before. It simplifies to:

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