SOLUTION: Rationalize the denominator sqrt(2x)/sqrt(x)-sqrt(10)

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Question 1192822: Rationalize the denominator
sqrt(2x)/sqrt(x)-sqrt(10)
Answer by math_tutor2020(3817) About Me  (Show Source):
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%28sqrt%282x%29%29%2F%28sqrt%28x%29-sqrt%2810%29%29 is in the form A%2F%28B-C%29

A+=+sqrt%282x%29

B+=+sqrt%28x%29

C+=+sqrt%2810%29

Multiply top and bottom by (B+C)
This way we have in the denominator, thereby rationalizing it (i.e. removing the square root terms from the denominator). Refer to the difference of squares rule.

A%2F%28B-C%29

%28A%28B%2BC%29%29%2F%28%28B-C%29%28B%2BC%29%29

%28A%28B%2BC%29%29%2F%28B%5E2+-+C%5E2%29

%28sqrt%282x%29%2A%28sqrt%28x%29%2Bsqrt%2810%29%29%29%2F%28x-10%29

%28sqrt%282x%29%2Asqrt%28x%29%2Bsqrt%282x%29%2Asqrt%2810%29%29%2F%28x-10%29

%28sqrt%282x%2Ax%29%2Bsqrt%282x%2A10%29%29%2F%28x-10%29

%28sqrt%282x%5E2%29%2Bsqrt%2820x%29%29%2F%28x-10%29

%28sqrt%28x%5E2%2A2%29%2Bsqrt%284%2A5x%29%29%2F%28x-10%29

%28sqrt%28x%5E2%29%2Asqrt%282%29%2Bsqrt%284%29%2Asqrt%285x%29%29%2F%28x-10%29

%28x%2Asqrt%282%29%2B2%2Asqrt%285x%29%29%2F%28x-10%29

Therefore,

such that x+%3E=+0 and x+%3C%3E+10