Rational Expressions help?

Question

Still confused on how to solve the following expressions: 

 

 

 

Directions: Simplify each expression and find the restrictions for each rational expression. 

 

A) (3)/(x-2) + (4/x) / (5)/(x-2) - (7)/(6x)

 

B) (5)/(x+3) / (2) + (1/x+3)

 

C) (3) / (a/a+5) - (a+5)/(a²)

 

D) (2/x) + (6) / (1/y) 

 

Thank you!

 

Answer 1

I'll do problem D) for you.  The others are done the same way.

 

D) 2/x + 6/(1/y)

 

     = 2/x + 6y             (When you divide by a fraction (1/y), invert the fraction and multiply)

 

     = 2/x + 6y*(x/x)    (Put the two terms over a common denominator (x))

 

     = 2/x + 6yx/x

 

     = (2+6yx)/x       (This is the final simplified answer)

 

In math, division by zero is undefined.  So any value of x or y that makes the denominator of a rational expression equal zero is not allowed.  In the simplified answer, the denominator is x, so x=0 is unallowed.  But in the original problem, there was also a 1/y, so y = 0 is also unallowed.  The restriction on the simplified answer then is x≠0 and y≠0.