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

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Answer 1 · 2017-03-21T01:59:40

$-(4+sqrt(15))$

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 $=((sqrt5+sqrt3)(sqrt3+sqrt5))/((sqrt3-sqrt5)(sqrt3+sqrt5))$

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

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

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

$=-(4+sqrt15)$

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