Solve 3-sqrt{x-1}=sqrt{4x+5}ft

$$3 - \sqrt { x - 1 } = \sqrt { 4 x + 5 } ft$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{\left(4x+5\right)^{-\frac{1}{2}}\left(\sqrt{x-1}-3\right)}{t}\text{, }&t\neq 0\text{ and }x\neq -\frac{5}{4}\\f\in \mathrm{C}\text{, }&x=10\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{4x+5}ft=3-\sqrt{x-1}$$

The equation is in standard form.

$$\sqrt{4x+5}tf=-\sqrt{x-1}+3$$

Divide both sides by \sqrt{4x+5}t.

$$\frac{\sqrt{4x+5}tf}{\sqrt{4x+5}t}=\frac{-\sqrt{x-1}+3}{\sqrt{4x+5}t}$$

Dividing by \sqrt{4x+5}t undoes the multiplication by \sqrt{4x+5}t.

$$f=\frac{-\sqrt{x-1}+3}{\sqrt{4x+5}t}$$

Divide 3-\sqrt{x-1} by \sqrt{4x+5}t.

$$f=\frac{\left(4x+5\right)^{-\frac{1}{2}}\left(-\sqrt{x-1}+3\right)}{t}$$

Solve for t (complex solution)

$$\left\{\begin{matrix}t=-\frac{\left(4x+5\right)^{-\frac{1}{2}}\left(\sqrt{x-1}-3\right)}{f}\text{, }&f\neq 0\text{ and }x\neq -\frac{5}{4}\\t\in \mathrm{C}\text{, }&x=10\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{4x+5}ft=3-\sqrt{x-1}$$

The equation is in standard form.

$$\sqrt{4x+5}ft=-\sqrt{x-1}+3$$

Divide both sides by \sqrt{4x+5}f.

$$\frac{\sqrt{4x+5}ft}{\sqrt{4x+5}f}=\frac{-\sqrt{x-1}+3}{\sqrt{4x+5}f}$$

Dividing by \sqrt{4x+5}f undoes the multiplication by \sqrt{4x+5}f.

$$t=\frac{-\sqrt{x-1}+3}{\sqrt{4x+5}f}$$

Divide 3-\sqrt{x-1} by \sqrt{4x+5}f.

$$t=\frac{\left(4x+5\right)^{-\frac{1}{2}}\left(-\sqrt{x-1}+3\right)}{f}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{\sqrt{x-1}-3}{\sqrt{4x+5}t}\text{, }&t\neq 0\text{ and }x\geq 1\\f\in \mathrm{R}\text{, }&t=0\text{ and }x=10\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{4x+5}ft=3-\sqrt{x-1}$$

The equation is in standard form.

$$\sqrt{4x+5}tf=-\sqrt{x-1}+3$$

Divide both sides by \sqrt{4x+5}t.

$$\frac{\sqrt{4x+5}tf}{\sqrt{4x+5}t}=\frac{-\sqrt{x-1}+3}{\sqrt{4x+5}t}$$

Dividing by \sqrt{4x+5}t undoes the multiplication by \sqrt{4x+5}t.

$$f=\frac{-\sqrt{x-1}+3}{\sqrt{4x+5}t}$$

Solve for t

$$\left\{\begin{matrix}t=-\frac{\sqrt{x-1}-3}{\sqrt{4x+5}f}\text{, }&f\neq 0\text{ and }x\geq 1\\t\in \mathrm{R}\text{, }&f=0\text{ and }x=10\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{4x+5}ft=3-\sqrt{x-1}$$

The equation is in standard form.

$$\sqrt{4x+5}ft=-\sqrt{x-1}+3$$

Divide both sides by \sqrt{4x+5}f.

$$\frac{\sqrt{4x+5}ft}{\sqrt{4x+5}f}=\frac{-\sqrt{x-1}+3}{\sqrt{4x+5}f}$$

Dividing by \sqrt{4x+5}f undoes the multiplication by \sqrt{4x+5}f.

$$t=\frac{-\sqrt{x-1}+3}{\sqrt{4x+5}f}$$