Solve Y=5x+5/x+5

$$Y = \frac{ 5x+5 }{ x+5 }$$

Solve for x

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

$$Y\neq 5$$

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.

$$Y\left(x+5\right)=5x+5$$

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

$$Yx+5Y=5x+5$$

Subtract 5x from both sides.

$$Yx+5Y-5x=5$$

Subtract 5Y from both sides.

$$Yx-5x=5-5Y$$

Combine all terms containing x.

$$\left(Y-5\right)x=5-5Y$$

Divide both sides by Y-5.

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

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

$$x=\frac{5-5Y}{Y-5}$$

Divide 5-5Y by Y-5.

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

Variable x cannot be equal to -5.

$$x=\frac{5\left(1-Y\right)}{Y-5}\text{, }x\neq -5$$

Solve for Y

$$Y=\frac{5\left(x+1\right)}{x+5}$$

$$x\neq -5$$