$$ \frac { a x - b + x - 9 } { a x ^ { 2 } + a b x } $$

Question

UpStudy AI · Accepted Answer

Let's simplify the given rational expression:

$$
\frac{a x - b + x - 9}{a x^{2} + a b x}
$$

**Step 1: Combine Like Terms**

First, combine the like terms in the numerator:

$$
a x + x - b - 9 = x(a + 1) - (b + 9)
$$

So, the expression becomes:

$$
\frac{x(a + 1) - (b + 9)}{a x^{2} + a b x}
$$

**Step 2: Factor the Denominator**

Factor the denominator by taking out the common factor $$ a x $$:

$$
a x^{2} + a b x = a x (x + b)
$$

**Step 3: Write the Simplified Expression**

Now, the expression is:

$$
\frac{x(a + 1) - (b + 9)}{a x (x + b)}
$$

**Final Simplified Form:**

$$
\boxed{\dfrac{(a + 1)x - (b + 9)}{a x (x + b)}}
$$

This is the simplified form of the original rational expression.
$$ \frac{(a + 1)x - (b + 9)}{a x (x + b)} $$

\( \frac { a x - b + x - 9 } { a x ^ { 2 } + a b x } \)