Solve for x -9/(x^2)+1=0

$- \frac{9}{x^{2}} + 1 = 0$

Subtract $1$ from both sides of the equation.

$- \frac{9}{x^{2}} = - 1$

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.

$x^{2}$

Multiply each term in $- \frac{9}{x^{2}} = - 1$ by $x^{2}$ to eliminate the fractions.

Multiply each term in $- \frac{9}{x^{2}} = - 1$ by $x^{2}$ .

$- \frac{9}{x^{2}} x^{2} = - x^{2}$

Simplify the left side.

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

Move the leading negative in $- \frac{9}{x^{2}}$ into the numerator.

$\frac{- 9}{x^{2}} x^{2} = - x^{2}$

Cancel the common factor.

$\frac{- 9}{x^{2}} x^{2} = - x^{2}$

Rewrite the expression.

$- 9 = - x^{2}$

Solve the equation.

Rewrite the equation as $- x^{2} = - 9$ .

$- x^{2} = - 9$

Divide each term in $- x^{2} = - 9$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 9$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 9}{- 1}$

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

$x^{2} = \frac{- 9}{- 1}$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$x^{2} = 9$

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

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$

Solve for x -9/(x^2)+1=0

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