How do you simplify #(sqrt5+sqrt3)/(sqrt3-sqrt5#?

1 Answer
Mar 21, 2017

Answer:

#-(4+sqrt(15))#

Explanation:

Expression #=(sqrt5+sqrt3)/(sqrt3-sqrt5#

To simplify the expression we first need to rationalise the denominator.

Remember: #(a+b)(a-b) = a^2-b^2#

Hence: #(sqrta+sqrtb)(sqrta-sqrtb) = a-b#

Multiply our expression by: #(sqrt3+sqrt5)/(sqrt3+sqrt5) =1#

#:.# Expression #=((sqrt5+sqrt3)(sqrt3+sqrt5))/((sqrt3-sqrt5)(sqrt3+sqrt5))#

#= ((sqrt5+sqrt3)(sqrt3+sqrt5))/ (3-5)#

#= (sqrt15+5+3+sqrt15)/-2#

#=(8+2sqrt15)/-2#

#=-(4+sqrt15)#