Question 623774
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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/x-1/(x+3)}}}
.
To simplify, we want to find a common denominator for x and x+3. Let's use x(x+3).
{{{(1/x)*((x+3)/(x+3))-(1/(x+3))*(x/x)}}}
{{{(x+3)/((x)(x+3))-x/((x)(x+3))}}}
{{{3/(x^2+3x)}}}

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

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