Solve y/4+3/x=9

$$\frac { y } { 4 } + \frac { 3 } { x } = 9$$

Solve for x

$$x=-\frac{12}{y-36}$$

$$y\neq 36$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4x, the least common multiple of 4,x.

$$xy+4\times 3=36x$$

Multiply 4 and 3 to get 12.

$$xy+12=36x$$

Subtract 36x from both sides.

$$xy+12-36x=0$$

Subtract 12 from both sides. Anything subtracted from zero gives its negation.

$$xy-36x=-12$$

Combine all terms containing x.

$$\left(y-36\right)x=-12$$

Divide both sides by y-36.

$$\frac{\left(y-36\right)x}{y-36}=-\frac{12}{y-36}$$

Dividing by y-36 undoes the multiplication by y-36.

$$x=-\frac{12}{y-36}$$

Variable x cannot be equal to 0.

$$x=-\frac{12}{y-36}\text{, }x\neq 0$$

Solve for y

$$y=36-\frac{12}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4x, the least common multiple of 4,x.

$$xy+4\times 3=36x$$

Multiply 4 and 3 to get 12.

$$xy+12=36x$$

Subtract 12 from both sides.

$$xy=36x-12$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{36x-12}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{36x-12}{x}$$

Divide 36x-12 by x.

$$y=36-\frac{12}{x}$$