Solve y=x+1/5-x

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

Solve for x

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

$$y\neq -1$$

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.

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

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

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

Subtract x from both sides.

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

Subtract 5y from both sides.

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

Combine all terms containing x.

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

Divide both sides by -y-1.

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

Dividing by -y-1 undoes the multiplication by -y-1.

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

Divide 1-5y by -y-1.

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

Variable x cannot be equal to 5.

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

Solve for y

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

$$x\neq 5$$