Solve 24+3y^2/2=12xy+6y^2/4

$$\frac{ 24+3 { y }^{ 2 } }{ 2 } = \frac{ 12xy+6 { y }^{ 2 } }{ 4 }$$

Solve for x

$$x=\frac{4}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(24+3y^{2}\right)=12xy+6y^{2}$$

Use the distributive property to multiply 2 by 24+3y^{2}.

$$48+6y^{2}=12xy+6y^{2}$$

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

$$12xy+6y^{2}=48+6y^{2}$$

Subtract 6y^{2} from both sides.

$$12xy=48+6y^{2}-6y^{2}$$

Combine 6y^{2} and -6y^{2} to get 0.

$$12xy=48$$

The equation is in standard form.

$$12yx=48$$

Divide both sides by 12y.

$$\frac{12yx}{12y}=\frac{48}{12y}$$

Dividing by 12y undoes the multiplication by 12y.

$$x=\frac{48}{12y}$$

Divide 48 by 12y.

$$x=\frac{4}{y}$$

Solve for y

$$y=\frac{4}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(24+3y^{2}\right)=12xy+6y^{2}$$

Use the distributive property to multiply 2 by 24+3y^{2}.

$$48+6y^{2}=12xy+6y^{2}$$

Subtract 12xy from both sides.

$$48+6y^{2}-12xy=6y^{2}$$

Subtract 6y^{2} from both sides.

$$48+6y^{2}-12xy-6y^{2}=0$$

Combine 6y^{2} and -6y^{2} to get 0.

$$48-12xy=0$$

Subtract 48 from both sides. Anything subtracted from zero gives its negation.

$$-12xy=-48$$

The equation is in standard form.

$$\left(-12x\right)y=-48$$

Divide both sides by -12x.

$$\frac{\left(-12x\right)y}{-12x}=-\frac{48}{-12x}$$

Dividing by -12x undoes the multiplication by -12x.

$$y=-\frac{48}{-12x}$$

Divide -48 by -12x.

$$y=\frac{4}{x}$$