Mathematics

Simplify (frac{5+sqrt{7}}{3+sqrt{7}})

Simplify (frac{5+sqrt{7}}{3+sqrt{7}})
  • A.
    17-√7
  • B.
    4-√7
  • C.
    15+√7
  • D.
    7-√7
Correct Answer: Option B
Explanation

(frac{5+sqrt{7}}{3+sqrt{7}}=frac{5+sqrt{7}}{3+sqrt{7}}times frac{3-sqrt{7}}{3-sqrt{7}}\
=frac{(5+sqrt{7})(3-sqrt{7})}{3^2 – sqrt{7}^2}\
=frac{15-5sqrt{7}+3sqrt{7}-7}{9-7}\
=frac{8-2sqrt{7}}{2})
Factorize then divide by 2
(=frac{2(4-sqrt{7}}{2}\
=4-sqrt{7})