Solve for x 8+(1/x-2)=16

$8 + (\frac{1}{x} - 2) = 16$

Step 1

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

Subtract $8$ from both sides of the equation.

$\frac{1}{x} - 2 = 16 - 8$

Add $2$ to both sides of the equation.

$\frac{1}{x} = 16 - 8 + 2$

Subtract $8$ from $16$ .

$\frac{1}{x} = 8 + 2$

Add $8$ and $2$ .

$\frac{1}{x} = 10$

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 $\frac{1}{x} = 10$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{1}{x} = 10$ by $x$ .

$\frac{1}{x} x = 10 x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{1}{x} x = 10 x$

Rewrite the expression.

$1 = 10 x$

Step 4

Solve the equation.

Rewrite the equation as $10 x = 1$ .

$10 x = 1$

Divide each term in $10 x = 1$ by $10$ and simplify.

Divide each term in $10 x = 1$ by $10$ .

$\frac{10 x}{10} = \frac{1}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 x}{10} = \frac{1}{10}$

Divide $x$ by $1$ .

$x = \frac{1}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{10}$

Decimal Form:

$x = 0.1$

Solve for x 8+(1/x-2)=16

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