Solve for x (7+x)/x=22

$\frac{7 + x}{x} = 22$

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 $\frac{7 + x}{x} = 22$ by $x$ to eliminate the fractions.

Multiply each term in $\frac{7 + x}{x} = 22$ by $x$ .

$\frac{7 + x}{x} x = 22 x$

Simplify the left side.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{7 + x}{x} x = 22 x$

Rewrite the expression.

$7 + x = 22 x$

Solve the equation.

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

Subtract $22 x$ from both sides of the equation.

$7 + x - 22 x = 0$

Subtract $22 x$ from $x$ .

$7 - 21 x = 0$

Subtract $7$ from both sides of the equation.

$- 21 x = - 7$

Divide each term in $- 21 x = - 7$ by $- 21$ and simplify.

Divide each term in $- 21 x = - 7$ by $- 21$ .

$\frac{- 21 x}{- 21} = \frac{- 7}{- 21}$

Simplify the left side.

Cancel the common factor of $- 21$ .

Cancel the common factor.

$\frac{- 21 x}{- 21} = \frac{- 7}{- 21}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 21}$

Simplify the right side.

Cancel the common factor of $- 7$ and $- 21$ .

Factor $- 7$ out of $- 7$ .

$x = \frac{- 7 (1)}{- 21}$

Cancel the common factors.

Factor $- 7$ out of $- 21$ .

$x = \frac{- 7 \cdot 1}{- 7 \cdot 3}$

Cancel the common factor.

$x = \frac{- 7 \cdot 1}{- 7 \cdot 3}$

Rewrite the expression.

$x = \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}$

Decimal Form:

$x = 0.\overline{3}$

Solve for x (7+x)/x=22

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