Answer to Question #228837 in Algebra for Benjamin

Question #228837

Simplify (√5+1)÷(√5-1)


1
Expert's answer
2021-08-25T07:48:06-0400

Answer:


To solve this problem we should multiply both numerator and denominator by  "\\frac{(\\sqrt{\\smash[b]{5}}+1)}{(\\sqrt{\\smash[b]{5}}+1)}" =1 (because multiplying any number by 1 doesn't change it) by itself to get a 'normal' number on the bottom. So in this case we do:


"\\frac{(\\sqrt{\\smash[b]{5}}+1)}{(\\sqrt{\\smash[b]{5}}-1)}*\\frac{(\\sqrt{\\smash[b]{5}}+1)}{(\\sqrt{\\smash[b]{5}}+1)}=\\frac{(\\sqrt{\\smash[b]{5}}*\\sqrt{\\smash[b]{5}}+\\sqrt{\\smash[b]{5}}+\\sqrt{\\smash[b]{5}}+1)}{(\\sqrt{\\smash[b]{5}}*\\sqrt{\\smash[b]{5}}+\\sqrt{\\smash[b]{5}}-\\sqrt{\\smash[b]{5}}-1)}=\\frac{(5+2\\sqrt{\\smash[b]{5}}+1)}{(5-1)}"


"\\implies \\frac{(5+2\\sqrt{\\smash[b]{5}}+1)}{(5-1)}=\\frac{(6+2\\sqrt{\\smash[b]{5}})}{(4)}=\\frac{2(3+\\sqrt{\\smash[b]{5}})}{4}=\\frac{3+\\sqrt{\\smash[b]{5}}}{2}"


Answer:

"\\frac{3+\\sqrt{\\smash[b]{5}}}{2}"



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