Prove that \[|xa|\left|\frac{1}{x}-\frac{1}{a}\right|=|x-a|.\]

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Lesson Parent: 
Rules of Absolute Values
Problem: 

Prove that \[|xa|\left|\frac{1}{x}-\frac{1}{a}\right|=|x-a|.\]

Answer: 

It is true that \[|xa|\left|\frac{1}{x}-\frac{1}{a}\right|=|x-a|.\]

SAMPLE SOLUTION

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Solution: 

First, because of this proof we know that

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And one of our rules of absolute values says for any two numbers $b$ and $c$ we have <Sign in to see all the formulas>. Therefore, <Sign in to see all the formulas>.

The proof is now complete.