Solve by Factoring 1/x=16/(9x)+7

$\frac{1}{x} = \frac{16}{9 x} + 7$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\frac{16}{9 x}$ from both sides of the equation.

$\frac{1}{x} - \frac{16}{9 x} = 7$

Subtract $7$ from both sides of the equation.

$\frac{1}{x} - \frac{16}{9 x} - 7 = 0$

Step 2

Simplify $\frac{1}{x} - \frac{16}{9 x} - 7$ .

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{1}{x} \cdot \frac{9}{9} - \frac{16}{9 x} - 7 = 0$

Write each expression with a common denominator of $x \cdot 9$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{x}$ by $\frac{9}{9}$ .

$\frac{9}{x \cdot 9} - \frac{16}{9 x} - 7 = 0$

Move $9$ to the left of $x$ .

$\frac{9}{9 x} - \frac{16}{9 x} - 7 = 0$

Combine the numerators over the common denominator.

$\frac{9 - 16}{9 x} - 7 = 0$

Subtract $16$ from $9$ .

$\frac{- 7}{9 x} - 7 = 0$

Move the negative in front of the fraction.

$- \frac{7}{9 x} - 7 = 0$

Step 3

Factor $- 7$ out of $- \frac{7}{9 x} - 7$ .

Factor $- 7$ out of $- \frac{7}{9 x}$ .

$- 7 (- \frac{- 1}{9 x}) - 7 = 0$

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

$- 7 (- \frac{- 1}{9 x}) - 7 \cdot 1 = 0$

Factor $- 7$ out of $- 7 (- \frac{- 1}{9 x}) - 7 (1)$ .

$- 7 (- \frac{- 1}{9 x} + 1) = 0$

Step 4

Move the negative in front of the fraction.

$- 7 (\frac{1}{9 x} + 1) = 0$

Step 5

Write $1$ as a fraction with a common denominator.

$- 7 (\frac{1}{9 x} + \frac{9 x}{9 x}) = 0$

Step 6

Combine the numerators over the common denominator.

$- 7 \frac{1 + 9 x}{9 x} = 0$

Step 7

Simplify $- 7 \frac{1 + 9 x}{9 x}$ .

Combine $- 7$ and $\frac{1 + 9 x}{9 x}$ .

$\frac{- 7 (1 + 9 x)}{9 x} = 0$

Move the negative in front of the fraction.

$- \frac{7 (1 + 9 x)}{9 x} = 0$

Step 8

Set the numerator equal to zero.

$7 (1 + 9 x) = 0$

Step 9

Solve the equation for $x$ .

Divide each term in $7 (1 + 9 x) = 0$ by $7$ and simplify.

Divide each term in $7 (1 + 9 x) = 0$ by $7$ .

$\frac{7 (1 + 9 x)}{7} = \frac{0}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 (1 + 9 x)}{7} = \frac{0}{7}$

Divide $1 + 9 x$ by $1$ .

$1 + 9 x = \frac{0}{7}$

Simplify the right side.

Divide $0$ by $7$ .

$1 + 9 x = 0$

Subtract $1$ from both sides of the equation.

$9 x = - 1$

Divide each term in $9 x = - 1$ by $9$ and simplify.

Divide each term in $9 x = - 1$ by $9$ .

$\frac{9 x}{9} = \frac{- 1}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 1}{9}$

Divide $x$ by $1$ .

$x = \frac{- 1}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{9}$

Solve by Factoring 1/x=16/(9x)+7

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