How do you rationalize the denominator and simplify x−42√x+7−7?

1 Answer
smendyka
Jul 3, 2017

See a solution process below:

Explanation:

To rationalize the denominator multiply the expression by 7−√x7−√x

7−√x7−√x×x−42√x+7−7⇒

7x−294−x√x+42√x7√x+49−x−7√x−7⇒

7x−294−x√x+42√x49−x−7

To subtract the 7 we need to put it over a common denominator:

7x−294−x√x+42√x49−x−(7×49−x49−x)⇒

7x−294−x√x+42√x49−x−343−7x49−x⇒

7x−294−x√x+42√x−343+7x49−x⇒

7x+7x−x√x+42√x−294−34349−x⇒

14x+(42−x)√x−63749−x

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