Solve for x y=1/(x^2)

$y = \frac{1}{x^{2}}$

Step 1

Rewrite the equation as $\frac{1}{x^{2}} = y$ .

$\frac{1}{x^{2}} = y$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x^{2}, 1$

The LCM of one and any expression is the expression.

$x^{2}$

Step 3

Multiply each term in $\frac{1}{x^{2}} = y$ by $x^{2}$ to eliminate the fractions.

Multiply each term in $\frac{1}{x^{2}} = y$ by $x^{2}$ .

$\frac{1}{x^{2}} x^{2} = y x^{2}$

Simplify the left side.

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{1}{x^{2}} x^{2} = y x^{2}$

Rewrite the expression.

$1 = y x^{2}$

Step 4

Solve the equation.

Rewrite the equation as $y x^{2} = 1$ .

$y x^{2} = 1$

Divide each term in $y x^{2} = 1$ by $y$ and simplify.

Divide each term in $y x^{2} = 1$ by $y$ .

$\frac{y x^{2}}{y} = \frac{1}{y}$

Simplify the left side.

Cancel the common factor of $y$ .

Cancel the common factor.

$\frac{y x^{2}}{y} = \frac{1}{y}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{1}{y}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{\frac{1}{y}}$

Simplify $\pm \sqrt{\frac{1}{y}}$ .

Rewrite $\sqrt{\frac{1}{y}}$ as $\frac{\sqrt{1}}{\sqrt{y}}$ .

$x = \pm \frac{\sqrt{1}}{\sqrt{y}}$

Any root of $1$ is $1$ .

$x = \pm \frac{1}{\sqrt{y}}$

Multiply $\frac{1}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$x = \pm \frac{1}{\sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}}$

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$x = \pm \frac{\sqrt{y}}{\sqrt{y} \sqrt{y}}$

Raise $\sqrt{y}$ to the power of $1$ .

$x = \pm \frac{\sqrt{y}}{{\sqrt{y}}^{1} \sqrt{y}}$

Raise $\sqrt{y}$ to the power of $1$ .

$x = \pm \frac{\sqrt{y}}{{\sqrt{y}}^{1} {\sqrt{y}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \pm \frac{\sqrt{y}}{{\sqrt{y}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$x = \pm \frac{\sqrt{y}}{{(y^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \pm \frac{\sqrt{y}}{y^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x = \pm \frac{\sqrt{y}}{y^{1}}$

Simplify.

$x = \pm \frac{\sqrt{y}}{y}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

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

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \frac{\sqrt{y}}{y}$

The complete solution is the result of both the positive and negative portions of the solution.

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

$x = - \frac{\sqrt{y}}{y}$

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

$x = - \frac{\sqrt{y}}{y}$

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

$x = - \frac{\sqrt{y}}{y}$

Solve for x y=1/(x^2)

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