Solve for x 4+(1/x-2)=20

$4 + (\frac{1}{x} - 2) = 20$

Step 1

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

Subtract $4$ from both sides of the equation.

$\frac{1}{x} - 2 = 20 - 4$

Add $2$ to both sides of the equation.

$\frac{1}{x} = 20 - 4 + 2$

Subtract $4$ from $20$ .

$\frac{1}{x} = 16 + 2$

Add $16$ and $2$ .

$\frac{1}{x} = 18$

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.

$x, 1$

The LCM of one and any expression is the expression.

$x$

Step 3

Multiply each term in $\frac{1}{x} = 18$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{1}{x} = 18$ by $x$ .

$\frac{1}{x} x = 18 x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{1}{x} x = 18 x$

Rewrite the expression.

$1 = 18 x$

Step 4

Solve the equation.

Rewrite the equation as $18 x = 1$ .

$18 x = 1$

Divide each term in $18 x = 1$ by $18$ and simplify.

Divide each term in $18 x = 1$ by $18$ .

$\frac{18 x}{18} = \frac{1}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 x}{18} = \frac{1}{18}$

Divide $x$ by $1$ .

$x = \frac{1}{18}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{18}$

Decimal Form:

$x = 0.0\overline{5}$

Solve for x 4+(1/x-2)=20

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