7/a^5+4/3a

Question

Simplify 7 divided by a to the fifth plus 4 divided by 3a

Answer 1

Hi Jim,

Without parentheses this expression means that the addition is done last, therefore the first thing to do is to modify the form of each of the two fractions so they each have the same denominator (bottom number).  You do this by multiplying each fraction by some form of 1.  For the first fraction multiply it by 3/3 giving you 21/3a⁵.  For the second fraction multiply it by a⁴/a⁴ giving you 4a⁴/3a⁵.  Notice that we have now converted each fraction to a form with 3a⁵ in the denominator and yet we've not changed the value of either fraction.  We've only changed the form; just like 2/4 and 1/2 are two forms of the same fraction.  Once the denominators are the same, the addition is simple:

 

21/3a⁵ + 4a⁴/3a⁵ = (21+4a⁴)/3a⁵

 

I hope this is helpful.

Charlie Gibson