Question

question evaluate the limit: $limlimits_{x \to 9} \frac{x - 9}{\frac{3}{2} - \frac{x + 9}{x + 3}}$ answer attempt 1 out of 2 dne submit answer

Explanation:

Step1: Simplify the denominator

First, we simplify the denominator $\frac{3}{2}-\frac{x + 9}{x + 3}$. Find a common denominator, which is $2(x + 3)$. Then we have:
$$\frac{3(x + 3)-2(x + 9)}{2(x + 3)}$$
Expand the numerator: $3x+9 - 2x - 18=\frac{x - 9}{2(x + 3)}$
So the original limit becomes:

$$\lim_{x ightarrow9}\frac{x - 9}{\frac{x - 9}{2(x + 3)}}$$

Step2: Cancel out common factors

We can cancel out the common factor of $x - 9$ (since $x
ightarrow9$ but $x
eq9$ at the limit point, so we can cancel):

$$\lim_{x ightarrow9}2(x + 3)$$

Step3: Substitute the limit value

Now substitute $x = 9$ into $2(x + 3)$:
$$2(9 + 3)=2\times12 = 24$$

Answer:

24