Simplify.
-$$\frac { 3 - \frac { 1 } { x } } { x + \frac { 1 } { 9 x } }$$

Question

Quizplus · Accepted Answer

To simplify the given expression, first find a common denominator for the fractions in the numerator and the denominator. For the numerator, the expression is $3 - \frac{1}{x}$, which can be rewritten as $\frac{3x}{x} - \frac{1}{x} = \frac{3x - 1}{x}$. For the denominator, the expression is $x + \frac{1}{9x}$, which can be rewritten as $\frac{9x^2}{9x} + \frac{1}{9x} = \frac{9x^2 + 1}{9x}$. Thus, the original expression becomes $\frac{\frac{3x - 1}{x}}{\frac{9x^2 + 1}{9x}}$. To simplify, multiply by the reciprocal of the denominator: $\frac{3x - 1}{x} \cdot \frac{9x}{9x^2 + 1}$. Simplifying this gives $\frac{9(3x - 1)}{9x^2 + 1}$, which matches choice A.

Simplify - 3−1xx+19x\frac { 3 - \frac { 1 } { x } } { x + \frac { 1 } { 9 x } }x+9x1​3−x1​​

Simplify
- $\frac { 3 - \frac { 1 } { x } } { x + \frac { 1 } { 9 x } }$