Solve 4x/(x+16)(x+4)=y

$$\frac { 4 x } { ( x + 16 ) ( x + 4 ) } = y$$

Solve for y

$$y=\frac{4x}{\left(x+4\right)\left(x+16\right)}$$

$$x\neq -16\text{ and }x\neq -4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x+4\right)\left(x+16\right).

$$4x=y\left(x+4\right)\left(x+16\right)$$

Use the distributive property to multiply y by x+4.

$$4x=\left(yx+4y\right)\left(x+16\right)$$

Use the distributive property to multiply yx+4y by x+16 and combine like terms.

$$4x=yx^{2}+20yx+64y$$

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

$$yx^{2}+20yx+64y=4x$$

Combine all terms containing y.

$$\left(x^{2}+20x+64\right)y=4x$$

Divide both sides by x^{2}+20x+64.

$$\frac{\left(x^{2}+20x+64\right)y}{x^{2}+20x+64}=\frac{4x}{x^{2}+20x+64}$$

Dividing by x^{2}+20x+64 undoes the multiplication by x^{2}+20x+64.

$$y=\frac{4x}{x^{2}+20x+64}$$

Divide 4x by x^{2}+20x+64.

$$y=\frac{4x}{\left(x+4\right)\left(x+16\right)}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{2\left(\sqrt{\left(y-1\right)\left(9y-1\right)}+5y-1\right)}{y}\text{; }x=-\frac{2\left(-\sqrt{\left(y-1\right)\left(9y-1\right)}+5y-1\right)}{y}\text{, }&y\geq 1\text{ or }\left(y\neq 0\text{ and }y\leq \frac{1}{9}\right)\\x=0\text{, }&y=0\end{matrix}\right.$$