Solve y=3x-1/x+5

$$y = \frac { 3 x - 1 } { x + 5 }$$

Solve for x

$$x=-\frac{5y+1}{y-3}$$

$$y\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to -5 since division by zero is not defined. Multiply both sides of the equation by x+5.

$$y\left(x+5\right)=3x-1$$

Use the distributive property to multiply y by x+5.

$$yx+5y=3x-1$$

Subtract 3x from both sides.

$$yx+5y-3x=-1$$

Subtract 5y from both sides.

$$yx-3x=-1-5y$$

Combine all terms containing x.

$$\left(y-3\right)x=-1-5y$$

The equation is in standard form.

$$\left(y-3\right)x=-5y-1$$

Divide both sides by y-3.

$$\frac{\left(y-3\right)x}{y-3}=\frac{-5y-1}{y-3}$$

Dividing by y-3 undoes the multiplication by y-3.

$$x=\frac{-5y-1}{y-3}$$

Divide -1-5y by y-3.

$$x=-\frac{5y+1}{y-3}$$

Variable x cannot be equal to -5.

$$x=-\frac{5y+1}{y-3}\text{, }x\neq -5$$

Solve for y

$$y=-\frac{1-3x}{x+5}$$

$$x\neq -5$$