SOLUTION: One number is thee more than another. Assume that the first number is x. Create a rational expression to represent the difference of the reciprocals of the two numbers. Simplify yo

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Question 623774: One number is thee more than another. Assume that the first number is x. Create a rational expression to represent the difference of the reciprocals of the two numbers. Simplify your answer.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--

The Problem:
One number is three more than another. Assume that the first number is x. Create a rational 
expression to represent the difference of the reciprocals of the two numbers. Simplify your answer.

A Solution:
Let x be the first number.

Since the second number is three more than the first, we can write it as x+3.

The reciprocal of x is 1/x.
The reciprocal of x+3 is 1/(x+3).

We can write the difference of the reciprocals as
1%2Fx-1%2F%28x%2B3%29
.
To simplify, we want to find a common denominator for x and x+3. Let's use x(x+3).
%281%2Fx%29%2A%28%28x%2B3%29%2F%28x%2B3%29%29-%281%2F%28x%2B3%29%29%2A%28x%2Fx%29
%28x%2B3%29%2F%28%28x%29%28x%2B3%29%29-x%2F%28%28x%29%28x%2B3%29%29
3%2F%28x%5E2%2B3x%29

Please email me if you have questions about the solution. I'd appreciate the feed back and I'd be 
glad to help you sort it out.

Ms.Figgy
math.in.the.vortex@gmail.com