Solve 3y-2/y+5=x

$$\frac { 3 y - 2 } { y + 5 } = x$$

Solve for x

$$x=\frac{3y-2}{y+5}$$

$$y\neq -5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y+5.

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

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

$$3y-2=xy+5x$$

Swap sides so that all variable terms are on the left hand side.

$$xy+5x=3y-2$$

Combine all terms containing x.

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

Divide both sides by y+5.

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

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

$$x=\frac{3y-2}{y+5}$$

Solve for y

$$y=\frac{5x+2}{3-x}$$

$$x\neq 3$$

Steps for Solving Linear Equation

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

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

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

$$3y-2=xy+5x$$

Subtract xy from both sides.

$$3y-2-xy=5x$$

Add 2 to both sides.

$$3y-xy=5x+2$$

Combine all terms containing y.

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

Divide both sides by 3-x.

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

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

$$y=\frac{5x+2}{3-x}$$

Variable y cannot be equal to -5.

$$y=\frac{5x+2}{3-x}\text{, }y\neq -5$$