Solve f(x)y=3x-5/2+4x

$$f ( x ) y = \frac { 3 x - 5 } { 2 + 4 x }$$

Solve for f (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(2x+1\right).

$$fxy\times 2\left(2x+1\right)=3x-5$$

Use the distributive property to multiply fxy\times 2 by 2x+1.

$$4fx^{2}y+fxy\times 2=3x-5$$

Combine all terms containing f.

$$\left(4x^{2}y+xy\times 2\right)f=3x-5$$

The equation is in standard form.

$$\left(2xy+4yx^{2}\right)f=3x-5$$

Divide both sides by 2xy+4yx^{2}.

$$\frac{\left(2xy+4yx^{2}\right)f}{2xy+4yx^{2}}=\frac{3x-5}{2xy+4yx^{2}}$$

Dividing by 2xy+4yx^{2} undoes the multiplication by 2xy+4yx^{2}.

$$f=\frac{3x-5}{2xy+4yx^{2}}$$

Divide 3x-5 by 2xy+4yx^{2}.

$$f=\frac{3x-5}{2xy\left(2x+1\right)}$$

Solve for f

$$\left\{\begin{matrix}f=-\frac{5-3x}{2xy\left(2x+1\right)}\text{, }&y\neq 0\text{ and }x\neq -\frac{1}{2}\text{ and }x\neq 0\\f\in \mathrm{R}\text{, }&y=0\text{ and }x=\frac{5}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(2x+1\right).

$$fxy\times 2\left(2x+1\right)=3x-5$$

Use the distributive property to multiply fxy\times 2 by 2x+1.

$$4fx^{2}y+fxy\times 2=3x-5$$

Combine all terms containing f.

$$\left(4x^{2}y+xy\times 2\right)f=3x-5$$

The equation is in standard form.

$$\left(2xy+4yx^{2}\right)f=3x-5$$

Divide both sides by 2xy+4yx^{2}.

$$\frac{\left(2xy+4yx^{2}\right)f}{2xy+4yx^{2}}=\frac{3x-5}{2xy+4yx^{2}}$$

Dividing by 2xy+4yx^{2} undoes the multiplication by 2xy+4yx^{2}.

$$f=\frac{3x-5}{2xy+4yx^{2}}$$

Divide 3x-5 by 2xy+4yx^{2}.

$$f=\frac{3x-5}{2xy\left(2x+1\right)}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{9+4\left(fy\right)^{2}-92fy}-2fy+3}{8fy}\text{; }x=\frac{-\sqrt{9+4\left(fy\right)^{2}-92fy}-2fy+3}{8fy}\text{, }&f\neq 0\text{ and }y\neq 0\\x=-\frac{5}{2fy-3}\text{, }&f=0\text{ or }y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{9+4\left(fy\right)^{2}-92fy}-2fy+3}{8fy}\text{; }x=\frac{-\sqrt{9+4\left(fy\right)^{2}-92fy}-2fy+3}{8fy}\text{, }&\left(f\geq \frac{8\sqrt{130}|y|+92y}{8y^{2}}\text{ or }f\leq -\frac{8\sqrt{130}|y|-92y}{8y^{2}}\right)\text{ and }f\neq 0\text{ and }y\neq 0\\x=-\frac{5}{2fy-3}\text{, }&f=0\text{ or }y=0\end{matrix}\right.$$