Question 709334: ((5x^-2)+(5y^-2))/((8x^-1)+(8y^-1))
Simplify the compound fractional expression. Give your answer in factored form. Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
This is a compound fraction because of the negative exponents. Let's rewrite the expression with positive exponents so we can see it better:
Different methods are taught on how to simplify this expression. One method is to
Combine the terms in both the numerator and the denominator of the "big" fraction
Turn the division into a multiplication by the reciprocal of the denominator
Simplify
But I prefer a different method:
Find the lowest common denominator (LCD) of all the "little" fractions.
Multiply the numerator and denominator of the "big" fraction by the LCD from step one.
The first method requires addition/subtraction of fractions. The second one does not which is a major reason I prefer it.
Using the second method...
The "little" denominators are , , x and y. The LCD of these 4 is: . Multiplying the numerator and denominator by this LCD:
To multiply correctly we need to use the Distributive Property:
In each "little" fraction the denominator cancels with all or some part of the LCD leaving:
There are no like terms here so we cannot simplify this further. But we might be able to reduce the fraction. To see if the fraction will reduce we must first factor the numerator and denominator:
There are no factors in common between the numerator and denominator so the fraction will not reduce.
The problem asks that the answer be left in factored form so our answer is:
(