Solve for a 2a-6/a=a

$2 a - \frac{6}{a} = a$

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.

$1, a, 1$

The LCM of one and any expression is the expression.

$a$

Multiply each term in $2 a - \frac{6}{a} = a$ by $a$ to eliminate the fractions.

Multiply each term in $2 a - \frac{6}{a} = a$ by $a$ .

$2 a \cdot a - \frac{6}{a} a = a \cdot a$

Simplify the left side.

Simplify each term.

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$2 (a \cdot a) - \frac{6}{a} a = a \cdot a$

Multiply $a$ by $a$ .

$2 a^{2} - \frac{6}{a} a = a \cdot a$

Cancel the common factor of $a$ .

Move the leading negative in $- \frac{6}{a}$ into the numerator.

$2 a^{2} + \frac{- 6}{a} a = a \cdot a$

Cancel the common factor.

$2 a^{2} + \frac{- 6}{a} a = a \cdot a$

Rewrite the expression.

$2 a^{2} - 6 = a \cdot a$

Simplify the right side.

Multiply $a$ by $a$ .

$2 a^{2} - 6 = a^{2}$

Solve the equation.

Move all terms containing $a$ to the left side of the equation.

Subtract $a^{2}$ from both sides of the equation.

$2 a^{2} - 6 - a^{2} = 0$

Subtract $a^{2}$ from $2 a^{2}$ .

$a^{2} - 6 = 0$

Add $6$ to both sides of the equation.

$a^{2} = 6$

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

$a = \pm \sqrt{6}$

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.

$a = \sqrt{6}$

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

$a = - \sqrt{6}$

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

$a = \sqrt{6}, - \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$a = \sqrt{6}, - \sqrt{6}$

Decimal Form:

$a = 2.44948974 \dots, - 2.44948974 \dots$

Solve for a 2a-6/a=a

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