How do you simplify (4 - sqrt 7) /(3+sqrt7)?

2 Answers
Jim G.
Jul 25, 2018

19/2-7/2sqrt7

Explanation:

"multiply the numerator/denominator by the conjugate of"
"the denominator"

"the conjugate of "3+sqrt7" is "3color(red)(-)sqrt7

=((4-sqrt7)(3-sqrt7))/((3+sqrt7)(3-sqrt7))

=(12-7sqrt7+7)/(9-7)

=(19-7sqrt7)/2=19/2-7/2sqrt7

Harish Chandra Rajpoot
Jul 25, 2018

frac{19-7\sqrt7}{2}

Explanation:

\frac{4-\sqrt7}{3+\sqrt7}

=\frac{(4-\sqrt7)(3-\sqrt7)}{(3+\sqrt7)(3-\sqrt7)}

=\frac{12-3\sqrt7-4\sqrt7+7}{3^2-(\sqrt7)^2}

=\frac{19-7\sqrt7}{9-7}

=\frac{19-7\sqrt7}{2}

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