SOLUTION: Tom showed the following work when he was asked to rationalize the denominator. Explain his mistakes and then show the correct work and answer. Rationalize: 3√𝑥 / √𝑥−

Algebra ->  Radicals -> SOLUTION: Tom showed the following work when he was asked to rationalize the denominator. Explain his mistakes and then show the correct work and answer. Rationalize: 3√𝑥 / √𝑥−      Log On


   



Question 1204737: Tom showed the following work when he was asked to rationalize the denominator. Explain his
mistakes and then show the correct work and answer.
Rationalize: 3√𝑥 / √𝑥−2 → 3√𝑥 / √𝑥−2 ∗ √𝑥−2 / √𝑥−2 = 3𝑥−6√𝑥 / 𝑥+4

Found 2 solutions by MathLover1, josgarithmetic:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
3sqrt%28x%29+%2F+sqrt%28x-2%29
%283sqrt%28x%29%2Fsqrt%28x-2%29%29%2A%28sqrt%28x-2%29%2Fsqrt%28x-2%29%29++....this part was correct
= %283sqrt%28x%29-6sqrt%28x%29+%29%2F+%28x%2B4%29...here Tom made mistake, he didn't multiply numerators nor denominators correctly


3sqrt%28x%29%2Fsqrt%28x-2%29

=%283sqrt%28x%29%2Fsqrt%28x-2%29%29%2A%28sqrt%28x-2%29%2Fsqrt%28x-2%29%29

=%283sqrt%28x%29%2Asqrt%28x-2%29%29%2F%28sqrt%28x-2%29%2Asqrt%28x-2%29%29

=%283sqrt%28x%29%2Asqrt%28x-2%29%29%2F%28sqrt%28x-2%29%29%5E2

=%283sqrt%28x%28x-2%29%29%29%2F%28x-2%29



Answer by josgarithmetic(39617) About Me  (Show Source):