Solve y=-2/x-3-4

$$y = \frac { - 2 } { x - 3 } - 4$$

Solve for x

$$x=\frac{3y+10}{y+4}$$

$$y\neq -4$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$y\left(x-3\right)=-2+\left(x-3\right)\left(-4\right)$$

Use the distributive property to multiply y by x-3.

$$yx-3y=-2+\left(x-3\right)\left(-4\right)$$

Use the distributive property to multiply x-3 by -4.

$$yx-3y=-2-4x+12$$

Add -2 and 12 to get 10.

$$yx-3y=10-4x$$

Add 4x to both sides.

$$yx-3y+4x=10$$

Add 3y to both sides.

$$yx+4x=10+3y$$

Combine all terms containing x.

$$\left(y+4\right)x=10+3y$$

The equation is in standard form.

$$\left(y+4\right)x=3y+10$$

Divide both sides by y+4.

$$\frac{\left(y+4\right)x}{y+4}=\frac{3y+10}{y+4}$$

Dividing by y+4 undoes the multiplication by y+4.

$$x=\frac{3y+10}{y+4}$$

Variable x cannot be equal to 3.

$$x=\frac{3y+10}{y+4}\text{, }x\neq 3$$

Solve for y

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

$$x\neq 3$$