Solve y=2/3x+2-1quadh

$$y = \frac { 2 } { 3 x + 2 } - 1 \quad h$$

Solve for h

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

$$x\neq -\frac{2}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3x+2.

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

Use the distributive property to multiply y by 3x+2.

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

Use the distributive property to multiply -h by 3x+2.

$$3yx+2y=2-3hx-2h$$

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

$$2-3hx-2h=3yx+2y$$

Subtract 2 from both sides.

$$-3hx-2h=3yx+2y-2$$

Combine all terms containing h.

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

The equation is in standard form.

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

Divide both sides by -3x-2.

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

Dividing by -3x-2 undoes the multiplication by -3x-2.

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

Divide 3yx+2y-2 by -3x-2.

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

Solve for x

$$x=\frac{2\left(1-h-y\right)}{3\left(y+h\right)}$$

$$y\neq -h$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by 3x+2.

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

Use the distributive property to multiply y by 3x+2.

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

Use the distributive property to multiply -h by 3x+2.

$$3yx+2y=2-3hx-2h$$

Add 3hx to both sides.

$$3yx+2y+3hx=2-2h$$

Subtract 2y from both sides.

$$3yx+3hx=2-2h-2y$$

Combine all terms containing x.

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

Divide both sides by 3y+3h.

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

Dividing by 3y+3h undoes the multiplication by 3y+3h.

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

Divide 2-2h-2y by 3y+3h.

$$x=\frac{2\left(1-h-y\right)}{3\left(y+h\right)}$$

Variable x cannot be equal to -\frac{2}{3}.

$$x=\frac{2\left(1-h-y\right)}{3\left(y+h\right)}\text{, }x\neq -\frac{2}{3}$$