Rationalize the denominator: \(\frac{1}{\sqrt{4-\sqrt{15}}} \cdot \frac{\sqrt{4-\sqrt{15}}}{\sqrt{4-\sqrt{15}}}=\frac{\sqrt{4-\sqrt{15}}}{4-\sqrt{15}}\).
\[\frac{\sqrt{4-\sqrt{15}}}{4-\sqrt{15}}-\frac{1}{\sqrt{4+\sqrt{15}}}\]
Rationalize the denominator: \(\frac{\sqrt{4-\sqrt{15}}}{4-\sqrt{15}} \cdot \frac{4+\sqrt{15}}{4+\sqrt{15}}=\frac{\sqrt{4-\sqrt{15}}(4+\sqrt{15})}{{4}^{2}-{\sqrt{15}}^{2}}\).
\[\frac{\sqrt{4-\sqrt{15}}(4+\sqrt{15})}{{4}^{2}-{\sqrt{15}}^{2}}-\frac{1}{\sqrt{4+\sqrt{15}}}\]
Simplify \({4}^{2}\) to \(16\).
\[\frac{\sqrt{4-\sqrt{15}}(4+\sqrt{15})}{16-{\sqrt{15}}^{2}}-\frac{1}{\sqrt{4+\sqrt{15}}}\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[\frac{\sqrt{4-\sqrt{15}}(4+\sqrt{15})}{16-15}-\frac{1}{\sqrt{4+\sqrt{15}}}\]
Simplify \(16-15\) to \(1\).
\[\frac{\sqrt{4-\sqrt{15}}(4+\sqrt{15})}{1}-\frac{1}{\sqrt{4+\sqrt{15}}}\]
Simplify \(\frac{\sqrt{4-\sqrt{15}}(4+\sqrt{15})}{1}\) to \((\sqrt{4-\sqrt{15}}(4+\sqrt{15}))\).
\[\sqrt{4-\sqrt{15}}(4+\sqrt{15})-\frac{1}{\sqrt{4+\sqrt{15}}}\]
Rationalize the denominator: \(\frac{1}{\sqrt{4+\sqrt{15}}} \cdot \frac{\sqrt{4+\sqrt{15}}}{\sqrt{4+\sqrt{15}}}=\frac{\sqrt{4+\sqrt{15}}}{4+\sqrt{15}}\).
\[\sqrt{4-\sqrt{15}}(4+\sqrt{15})-\frac{\sqrt{4+\sqrt{15}}}{4+\sqrt{15}}\]
Rationalize the denominator: \(\frac{\sqrt{4+\sqrt{15}}}{4+\sqrt{15}} \cdot \frac{4-\sqrt{15}}{4-\sqrt{15}}=\frac{\sqrt{4+\sqrt{15}}(4-\sqrt{15})}{{4}^{2}-{\sqrt{15}}^{2}}\).
\[\sqrt{4-\sqrt{15}}(4+\sqrt{15})-\frac{\sqrt{4+\sqrt{15}}(4-\sqrt{15})}{{4}^{2}-{\sqrt{15}}^{2}}\]
Simplify \({4}^{2}\) to \(16\).
\[\sqrt{4-\sqrt{15}}(4+\sqrt{15})-\frac{\sqrt{4+\sqrt{15}}(4-\sqrt{15})}{16-{\sqrt{15}}^{2}}\]
Use this rule: \({\sqrt{x}}^{2}=x\).
\[\sqrt{4-\sqrt{15}}(4+\sqrt{15})-\frac{\sqrt{4+\sqrt{15}}(4-\sqrt{15})}{16-15}\]
Simplify \(16-15\) to \(1\).
\[\sqrt{4-\sqrt{15}}(4+\sqrt{15})-\frac{\sqrt{4+\sqrt{15}}(4-\sqrt{15})}{1}\]
Simplify \(\frac{\sqrt{4+\sqrt{15}}(4-\sqrt{15})}{1}\) to \((\sqrt{4+\sqrt{15}}(4-\sqrt{15}))\).
\[\sqrt{4-\sqrt{15}}(4+\sqrt{15})-\sqrt{4+\sqrt{15}}(4-\sqrt{15})\]
Decimal Form: 2.449490
sqrt(4-sqrt(15))*(4+sqrt(15))-sqrt(4+sqrt(15))*(4-sqrt(15))
