If frac{sqrt{5+x}+sqrt{5-x}}{sqrt{5+x}-sqrt{5 | vedclass

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(D) Given the equation: $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$Applying the Componendo and Dividendo rule,which states that if $\frac{

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$3$

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(D) Given the equation: $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$Applying the Componendo and Dividendo rule,which states that if $\frac{a}{b} = \frac{c}{d}$,then $\frac{a+b}{a-b} = \frac{c+d}{c-d}$:Let $a = \sqrt{5+x}+\sqrt{5-x}$ and $b = \sqrt{5+x}-\sqrt{5-x}$.Then $\frac{(\sqrt{5+x}+\sqrt{5-x}) + (\sqrt{5+x}-\sqrt{5-x})}{(\sqrt{5+x}+\sqrt{5-x}) - (\sqrt{5+x}-\sqrt{5-x})} = \frac{3+1}{3-1}$Simplifying the numerator and denominator:$\frac{2\sqrt{5+x}}{2\sqrt{5-x}} = \frac{4}{2}$$\frac{\sqrt{5+x}}{\sqrt{5-x}} = 2$Squaring both sides:$\frac{5+x}{5-x} = 4$$5+x = 4(5-x)$$5+x = 20 - 4x$$5x = 15$$x = 3$Thus,the value of $x$ is $3$.

If $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3,$ then what is the value of $x?$

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