Solve for x 3+(1/x-2)=27

$3 + (\frac{1}{x} - 2) = 27$

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$\frac{1}{x} - 2 = 27 - 3$

Add $2$ to both sides of the equation.

$\frac{1}{x} = 27 - 3 + 2$

Subtract $3$ from $27$ .

$\frac{1}{x} = 24 + 2$

Add $24$ and $2$ .

$\frac{1}{x} = 26$

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.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Multiply each term in $\frac{1}{x} = 26$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{1}{x} = 26$ by $x$ .

$\frac{1}{x} x = 26 x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{1}{x} x = 26 x$

Rewrite the expression.

$1 = 26 x$

Solve the equation.

Rewrite the equation as $26 x = 1$ .

$26 x = 1$

Divide each term in $26 x = 1$ by $26$ and simplify.

Divide each term in $26 x = 1$ by $26$ .

$\frac{26 x}{26} = \frac{1}{26}$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 x}{26} = \frac{1}{26}$

Divide $x$ by $1$ .

$x = \frac{1}{26}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{26}$

Decimal Form:

$x = 0.0\overline{384615}$