Solve 2y(y+3)/y(y-2)=9x/3x

$$\frac { 2 y ( y + 3 ) } { y ( y - 2 ) } = \frac { 9 x } { 3 x }$$

Solve for x

$$x\neq 0$$

$$y=12$$

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 3xy\left(y-2\right), the least common multiple of y\left(y-2\right),3x.

$$3x\times 2y\left(y+3\right)=y\left(y-2\right)\times 9x$$

Multiply 3 and 2 to get 6.

$$6xy\left(y+3\right)=y\left(y-2\right)\times 9x$$

Use the distributive property to multiply 6xy by y+3.

$$6xy^{2}+18yx=y\left(y-2\right)\times 9x$$

Use the distributive property to multiply y by y-2.

$$6xy^{2}+18yx=\left(y^{2}-2y\right)\times 9x$$

Use the distributive property to multiply y^{2}-2y by 9.

$$6xy^{2}+18yx=\left(9y^{2}-18y\right)x$$

Use the distributive property to multiply 9y^{2}-18y by x.

$$6xy^{2}+18yx=9y^{2}x-18yx$$

Subtract 9y^{2}x from both sides.

$$6xy^{2}+18yx-9y^{2}x=-18yx$$

Combine 6xy^{2} and -9y^{2}x to get -3xy^{2}.

$$-3xy^{2}+18yx=-18yx$$

Add 18yx to both sides.

$$-3xy^{2}+18yx+18yx=0$$

Combine 18yx and 18yx to get 36yx.

$$-3xy^{2}+36yx=0$$

Combine all terms containing x.

$$\left(-3y^{2}+36y\right)x=0$$

The equation is in standard form.

$$\left(36y-3y^{2}\right)x=0$$

Divide 0 by -3y^{2}+36y.

$$x=0$$

Variable x cannot be equal to 0.

$$x\in \emptyset$$

Solve for y

$$y=12$$

$$x\neq 0$$