Solve y=3x/xdiv6x^2/y

$$y = \frac { 3 x } { x } \div \frac { 6 x ^ { 2 } } { y }$$

Solve for y (complex solution)

$$y\neq 0$$

$$x=-\frac{\sqrt{2}}{2}\text{ or }x=\frac{\sqrt{2}}{2}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Divide \frac{3x}{x} by \frac{6x^{2}}{y} by multiplying \frac{3x}{x} by the reciprocal of \frac{6x^{2}}{y}.

$$y=\frac{3xy}{x\times 6x^{2}}$$

Cancel out 3x in both numerator and denominator.

$$y=\frac{y}{2x^{2}}$$

Subtract \frac{y}{2x^{2}} from both sides.

$$y-\frac{y}{2x^{2}}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{2x^{2}}{2x^{2}}.

$$\frac{y\times 2x^{2}}{2x^{2}}-\frac{y}{2x^{2}}=0$$

Since \frac{y\times 2x^{2}}{2x^{2}} and \frac{y}{2x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y\times 2x^{2}-y}{2x^{2}}=0$$

Multiply both sides of the equation by 2x^{2}.

$$y\times 2x^{2}-y=0$$

Combine all terms containing y.

$$\left(2x^{2}-1\right)y=0$$

Divide 0 by 2x^{2}-1.

$$y=0$$

Variable y cannot be equal to 0.

$$y\in \emptyset$$

Solve for y

$$y\neq 0$$

$$x = \frac{\sqrt{2}}{2} = 0.7071067811865476$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Divide \frac{3x}{x} by \frac{6x^{2}}{y} by multiplying \frac{3x}{x} by the reciprocal of \frac{6x^{2}}{y}.

$$y=\frac{3xy}{x\times 6x^{2}}$$

Cancel out 3x in both numerator and denominator.

$$y=\frac{y}{2x^{2}}$$

Subtract \frac{y}{2x^{2}} from both sides.

$$y-\frac{y}{2x^{2}}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{2x^{2}}{2x^{2}}.

$$\frac{y\times 2x^{2}}{2x^{2}}-\frac{y}{2x^{2}}=0$$

Since \frac{y\times 2x^{2}}{2x^{2}} and \frac{y}{2x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{y\times 2x^{2}-y}{2x^{2}}=0$$

Multiply both sides of the equation by 2x^{2}.

$$y\times 2x^{2}-y=0$$

Combine all terms containing y.

$$\left(2x^{2}-1\right)y=0$$

Divide 0 by 2x^{2}-1.

$$y=0$$

Variable y cannot be equal to 0.

$$y\in \emptyset$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781\text{, }y\neq 0$$

Solve for x

$$x = \frac{\sqrt{2}}{2} = 0.7071067811865476$$

$$x=-\frac{\sqrt{2}}{2}\text{, }y\neq 0$$