What is the value of left[frac{12}{(sqrt{5}+s | vedclass

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(B) To solve the expression $\left[\frac{12}{(\sqrt{5}+\sqrt{3})}+\frac{18}{(\sqrt{5}-\sqrt{3})}\right]$,we rationalize the denominators.Step $1$: Rat

Vedclass · Accepted Answer

$3(5 \sqrt{5}+\sqrt{3})$

Vedclass · Answer

(B) To solve the expression $\left[\frac{12}{(\sqrt{5}+\sqrt{3})}+\frac{18}{(\sqrt{5}-\sqrt{3})}ight]$,we rationalize the denominators.Step $1$: Rationalize the first term $\frac{12}{(\sqrt{5}+\sqrt{3})}$.$\frac{12}{(\sqrt{5}+\sqrt{3})} 	imes \frac{(\sqrt{5}-\sqrt{3})}{(\sqrt{5}-\sqrt{3})} = \frac{12(\sqrt{5}-\sqrt{3})}{5-3} = \frac{12(\sqrt{5}-\sqrt{3})}{2} = 6(\sqrt{5}-\sqrt{3}) = 6\sqrt{5}-6\sqrt{3}$.Step $2$: Rationalize the second term $\frac{18}{(\sqrt{5}-\sqrt{3})}$.$\frac{18}{(\sqrt{5}-\sqrt{3})} 	imes \frac{(\sqrt{5}+\sqrt{3})}{(\sqrt{5}+\sqrt{3})} = \frac{18(\sqrt{5}+\sqrt{3})}{5-3} = \frac{18(\sqrt{5}+\sqrt{3})}{2} = 9(\sqrt{5}+\sqrt{3}) = 9\sqrt{5}+9\sqrt{3}$.Step $3$: Add the two results.$(6\sqrt{5}-6\sqrt{3}) + (9\sqrt{5}+9\sqrt{3}) = (6+9)\sqrt{5} + (9-6)\sqrt{3} = 15\sqrt{5} + 3\sqrt{3}$.Step $4$: Factor out $3$ from the expression.$3(5\sqrt{5} + \sqrt{3})$.Thus,the correct option is $B$.

What is the value of $\left[\frac{12}{(\sqrt{5}+\sqrt{3})}+\frac{18}{(\sqrt{5}-\sqrt{3})}\right]$?

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