Simplify \(2\sqrt{2}f\imath nd\sqrt{x}\) to \(2\imath fnd\sqrt{2x}\).
\[Ifx=3+2\imath fnd\sqrt{2x}-\frac{1}{\sqrt{x}}\]
Subtract \(3\) from both sides.
\[Ifx-3=2\imath fnd\sqrt{2x}-\frac{1}{\sqrt{x}}\]
Regroup terms.
\[Ifx-3=-\frac{1}{\sqrt{x}}+2\imath fnd\sqrt{2x}\]
Add \(\frac{1}{\sqrt{x}}\) to both sides.
\[Ifx-3+\frac{1}{\sqrt{x}}=2\imath fnd\sqrt{2x}\]
Divide both sides by \(2\).
\[\frac{Ifx-3+\frac{1}{\sqrt{x}}}{2}=\imath fnd\sqrt{2x}\]
Simplify \(\frac{Ifx-3+\frac{1}{\sqrt{x}}}{2}\) to \(\frac{Ifx}{2}-\frac{3}{2}+\frac{\frac{1}{\sqrt{x}}}{2}\).
\[\frac{Ifx}{2}-\frac{3}{2}+\frac{\frac{1}{\sqrt{x}}}{2}=\imath fnd\sqrt{2x}\]
Simplify \(\frac{\frac{1}{\sqrt{x}}}{2}\) to \(\frac{1}{2\sqrt{x}}\).
\[\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}}=\imath fnd\sqrt{2x}\]
Divide both sides by \(\imath \).
\[\frac{\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}}}{\imath }=fnd\sqrt{2x}\]
Rationalize the denominator: \(\frac{\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}}}{\imath } \cdot \frac{\imath }{\imath }=-(\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})\imath \).
\[-(\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})\imath =fnd\sqrt{2x}\]
Regroup terms.
\[-\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})=fnd\sqrt{2x}\]
Divide both sides by \(f\).
\[-\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{f}=nd\sqrt{2x}\]
Divide both sides by \(d\).
\[-\frac{\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{f}}{d}=n\sqrt{2x}\]
Simplify \(\frac{\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{f}}{d}\) to \(\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{fd}\).
\[-\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{fd}=n\sqrt{2x}\]
Divide both sides by \(\sqrt{2x}\).
\[-\frac{\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{fd}}{\sqrt{2x}}=n\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[-\frac{\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{fd}}{\sqrt{2}\sqrt{x}}=n\]
Simplify \(\frac{\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{fd}}{\sqrt{2}\sqrt{x}}\) to \(\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{\sqrt{2}fd\sqrt{x}}\).
\[-\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{\sqrt{2}fd\sqrt{x}}=n\]
Switch sides.
\[n=-\frac{\imath (\frac{Ifx}{2}-\frac{3}{2}+\frac{1}{2\sqrt{x}})}{\sqrt{2}fd\sqrt{x}}\]
n=-(IM*((If*x)/2-3/2+1/(2*sqrt(x))))/(sqrt(2)*f*d*sqrt(x))
