Solve {l}{y=5/x-3-2}{text{Solvefor}ztext{where}}{z=xoperatorname{in}(2,5)}

$$\left. \begin{array} { l } { y = \frac{5}{x - 3} - 2 }\\ { \text{Solve for } z \text{ where} } \\ { z = x \operatorname{in}(2, 5) } \end{array} \right.$$

Solve for x

$$x=\frac{3y+11}{y+2}$$

$$y\neq -2$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$y\left(x-3\right)=5+\left(x-3\right)\left(-2\right)$$

Use the distributive property to multiply y by x-3.

$$yx-3y=5+\left(x-3\right)\left(-2\right)$$

Use the distributive property to multiply x-3 by -2.

$$yx-3y=5-2x+6$$

Add 5 and 6 to get 11.

$$yx-3y=11-2x$$

Add 2x to both sides.

$$yx-3y+2x=11$$

Add 3y to both sides.

$$yx+2x=11+3y$$

Combine all terms containing x.

$$\left(y+2\right)x=11+3y$$

The equation is in standard form.

$$\left(y+2\right)x=3y+11$$

Divide both sides by y+2.

$$\frac{\left(y+2\right)x}{y+2}=\frac{3y+11}{y+2}$$

Dividing by y+2 undoes the multiplication by y+2.

$$x=\frac{3y+11}{y+2}$$

Variable x cannot be equal to 3.

$$x=\frac{3y+11}{y+2}\text{, }x\neq 3$$