How do you simplify $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{3} - \sqrt{5}}$ $(sqrt5+sqrt3)/(sqrt3-sqrt5$ ?

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Answer 1 · 2017-03-21T01:59:40

$- (4 + \sqrt{15})$ $-(4+sqrt(15))$

Expression $= \frac{\sqrt{5} + \sqrt{3}}{\sqrt{3} - \sqrt{5}}$ $=(sqrt5+sqrt3)/(sqrt3-sqrt5$

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

Remember: $(a + b) (a - b) = a^{2} - b^{2}$ $(a+b)(a-b) = a^2-b^2$

Hence: $(\sqrt{a} + \sqrt{b}) (\sqrt{a} - \sqrt{b}) = a - b$ $(sqrta+sqrtb)(sqrta-sqrtb) = a-b$

Multiply our expression by: $\frac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}} = 1$ $(sqrt3+sqrt5)/(sqrt3+sqrt5) =1$

$:.$ 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√5+√3√3−√5(sqrt5+sqrt3)/(sqrt3-sqrt5?