Solve wfx=2x^2-3x+1/x+3

$$wfx = \frac{ 2 { x }^{ 2 } -3x+1 }{ x+3 }$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=-\frac{\left(1-x\right)\left(2x-1\right)}{wx\left(x+3\right)}\text{, }&x\neq -3\text{ and }x\neq 0\text{ and }w\neq 0\\f\in \mathrm{C}\text{, }&\left(x=\frac{1}{2}\text{ or }x=1\right)\text{ and }w=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+3.

$$wfx\left(x+3\right)=2x^{2}-3x+1$$

Use the distributive property to multiply wfx by x+3.

$$wfx^{2}+3wfx=2x^{2}-3x+1$$

Combine all terms containing f.

$$\left(wx^{2}+3wx\right)f=2x^{2}-3x+1$$

Divide both sides by wx^{2}+3wx.

$$\frac{\left(wx^{2}+3wx\right)f}{wx^{2}+3wx}=\frac{\left(x-1\right)\left(2x-1\right)}{wx^{2}+3wx}$$

Dividing by wx^{2}+3wx undoes the multiplication by wx^{2}+3wx.

$$f=\frac{\left(x-1\right)\left(2x-1\right)}{wx^{2}+3wx}$$

Divide \left(-1+x\right)\left(-1+2x\right) by wx^{2}+3wx.

$$f=\frac{\left(x-1\right)\left(2x-1\right)}{wx\left(x+3\right)}$$

Solve for w (complex solution)

$$\left\{\begin{matrix}w=-\frac{\left(1-x\right)\left(2x-1\right)}{fx\left(x+3\right)}\text{, }&x\neq -3\text{ and }x\neq 0\text{ and }f\neq 0\\w\in \mathrm{C}\text{, }&\left(x=\frac{1}{2}\text{ or }x=1\right)\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+3.

$$wfx\left(x+3\right)=2x^{2}-3x+1$$

Use the distributive property to multiply wfx by x+3.

$$wfx^{2}+3wfx=2x^{2}-3x+1$$

Combine all terms containing w.

$$\left(fx^{2}+3fx\right)w=2x^{2}-3x+1$$

Divide both sides by 3xf+fx^{2}.

$$\frac{\left(fx^{2}+3fx\right)w}{fx^{2}+3fx}=\frac{\left(x-1\right)\left(2x-1\right)}{fx^{2}+3fx}$$

Dividing by 3xf+fx^{2} undoes the multiplication by 3xf+fx^{2}.

$$w=\frac{\left(x-1\right)\left(2x-1\right)}{fx^{2}+3fx}$$

Divide \left(-1+x\right)\left(-1+2x\right) by 3xf+fx^{2}.

$$w=\frac{\left(x-1\right)\left(2x-1\right)}{fx\left(x+3\right)}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{\left(1-x\right)\left(2x-1\right)}{wx\left(x+3\right)}\text{, }&x\neq -3\text{ and }x\neq 0\text{ and }w\neq 0\\f\in \mathrm{R}\text{, }&\left(x=\frac{1}{2}\text{ or }x=1\right)\text{ and }w=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+3.

$$wfx\left(x+3\right)=2x^{2}-3x+1$$

Use the distributive property to multiply wfx by x+3.

$$wfx^{2}+3wfx=2x^{2}-3x+1$$

Combine all terms containing f.

$$\left(wx^{2}+3wx\right)f=2x^{2}-3x+1$$

Divide both sides by wx^{2}+3wx.

$$\frac{\left(wx^{2}+3wx\right)f}{wx^{2}+3wx}=\frac{\left(x-1\right)\left(2x-1\right)}{wx^{2}+3wx}$$

Dividing by wx^{2}+3wx undoes the multiplication by wx^{2}+3wx.

$$f=\frac{\left(x-1\right)\left(2x-1\right)}{wx^{2}+3wx}$$

Divide \left(-1+x\right)\left(-1+2x\right) by wx^{2}+3wx.

$$f=\frac{\left(x-1\right)\left(2x-1\right)}{wx\left(x+3\right)}$$

Solve for w

$$\left\{\begin{matrix}w=-\frac{\left(1-x\right)\left(2x-1\right)}{fx\left(x+3\right)}\text{, }&x\neq -3\text{ and }x\neq 0\text{ and }f\neq 0\\w\in \mathrm{R}\text{, }&\left(x=\frac{1}{2}\text{ or }x=1\right)\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+3.

$$wfx\left(x+3\right)=2x^{2}-3x+1$$

Use the distributive property to multiply wfx by x+3.

$$wfx^{2}+3wfx=2x^{2}-3x+1$$

Combine all terms containing w.

$$\left(fx^{2}+3fx\right)w=2x^{2}-3x+1$$

Divide both sides by 3xf+fx^{2}.

$$\frac{\left(fx^{2}+3fx\right)w}{fx^{2}+3fx}=\frac{\left(x-1\right)\left(2x-1\right)}{fx^{2}+3fx}$$

Dividing by 3xf+fx^{2} undoes the multiplication by 3xf+fx^{2}.

$$w=\frac{\left(x-1\right)\left(2x-1\right)}{fx^{2}+3fx}$$

Divide \left(-1+x\right)\left(-1+2x\right) by 3xf+fx^{2}.

$$w=\frac{\left(x-1\right)\left(2x-1\right)}{fx\left(x+3\right)}$$