Solve y=5x-2/x+1

$$y = \frac { 5 x - 2 } { x + 1 }$$

Solve for x

$$x=-\frac{y+2}{y-5}$$

$$y\neq 5$$

Steps for Solving Linear Equation

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by x+1.

$$y\left(x+1\right)=5x-2$$

Use the distributive property to multiply y by x+1.

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

Subtract 5x from both sides.

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

Subtract y from both sides.

$$yx-5x=-2-y$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y-5.

$$\frac{\left(y-5\right)x}{y-5}=\frac{-y-2}{y-5}$$

Dividing by y-5 undoes the multiplication by y-5.

$$x=\frac{-y-2}{y-5}$$

Divide -2-y by y-5.

$$x=-\frac{y+2}{y-5}$$

Variable x cannot be equal to -1.

$$x=-\frac{y+2}{y-5}\text{, }x\neq -1$$

Solve for y

$$y=-\frac{2-5x}{x+1}$$

$$x\neq -1$$