Perform the operation indicated. Simplify. $$ \frac{x-y}{x y}-\frac{9-y}{9 y} $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{x - y}{x y} - \frac{9 - y}{9 y}
$$

**Step 1: Find a Common Denominator**

The denominators are $$x y$$ and $$9 y$$. The least common denominator (LCD) is $$9 x y$$.

**Step 2: Rewrite Each Fraction with the LCD**

$$
\frac{x - y}{x y} = \frac{9(x - y)}{9 x y}
$$
$$
\frac{9 - y}{9 y} = \frac{x(9 - y)}{9 x y}
$$

**Step 3: Subtract the Fractions**

$$
\frac{9(x - y) - x(9 - y)}{9 x y}
$$

**Step 4: Simplify the Numerator**

Expand and combine like terms:

$$
9x - 9y - 9x + x y = x y - 9 y = y(x - 9)
$$

**Step 5: Cancel Common Factors**

$$
\frac{y(x - 9)}{9 x y} = \frac{x - 9}{9 x}
$$

**Final Simplified Expression:**

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

**Answer:** After simplifying, the expression is (x – 9) divided by (9 × x). Thus,

(x − 9)/(9 x)
$$ \frac{x - 9}{9x} $$

Perform the operation indicated. Simplify. \( \frac{x-y}{x y}-\frac{9-y}{9 y} \)