Reduce the expression [2(sqrt(x-3))] / [2(sqrt(x+3))]

[lroxy2]

The problem says to reduce the expression.

[2(sqrt(x-3))] / [2(sqrt(x+3))]

My first thought was to find a common denominator which would be [2(sqrt(x+3))] and multiply both the top and bottom of the fraction by the common denominator.

But my other thought was to square both the top and bottom of the fraction but I do not know if that is allowed.

 

[morson]

A "common denominator"? A denominator common to which fractions? There seems to be only one.

First, cancel the 2's. Then I suppose it's just sqrt[(x-3)/(x+3)]? Which could be written "sqrt[1 - 6/(x+3)]." This is true so long as x isn't -3.

 

[lroxy2]

Thank you for your input! I am still a little confused, where do the 1 & 6 come from? Are they under the square root sign? And are they together over the (x-3)?

 

[morson]

Sorry.

I meant \(\displaystyle \sqrt{1 - \frac{6}{x+3}\\\)

This is the case because \(\displaystyle \frac{x-3}{x+3}\\) has a remainder of -6 and a quotient of 1. See "polynomial division."

By the way,

\(\displaystyle x \not= -3\)