SOLUTION: Simplify {{{sqrt(20)/5-1/sqrt(5)}}}

Question 117122: Simplify

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Multiply the second fraction by . Doing this will make
the denominator a rational number

Combine the fractions

Multiply to get . Notice how shows
how the square undoes the square root.

Now that we have a rational denominator, and also a common denominator, we can combine the fractions

Combine the numerators

Factor 20 into 4*5

Break up the roots using the identity .

Take the square root of the perfect square 4 to get 2

Notice how we have the common term

Combine like terms

Combine like terms

So simplifies to . In other words, .

So looking at the answer you wrote, you are correct since is equivalent to

Check:

If we evaluate with a calculator, we get

and if we evaluate with a calculator, we get

Notice how these evaluate to the same value. So this shows that and this verifies our
answer.
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