Let's solve the expression step-by-step for [tex]\( x = 9 \)[/tex]:
First, substitute [tex]\( x = 9 \)[/tex] into the expression [tex]\(\frac{(x+3)(x-1)}{(x-5)}\)[/tex]:
1. Calculate the value of [tex]\( x + 3 \)[/tex] :
[tex]\[
x + 3 = 9 + 3 = 12
\][/tex]
2. Calculate the value of [tex]\( x - 1 \)[/tex] :
[tex]\[
x - 1 = 9 - 1 = 8
\][/tex]
3. Calculate the value of [tex]\( x - 5 \)[/tex] :
[tex]\[
x - 5 = 9 - 5 = 4
\][/tex]
Now, substitute these values back into the expression:
4. Calculate the numerator [tex]\((x+3)(x-1) :
\[
(x + 3)(x - 1) = 12 \times 8 = 96
\]
5. Calculate the denominator \((x-5) :
\[
(x-5) = 4
\]
6. Divide the numerator by the denominator to find the result:
\[
\frac{(x+3)(x-1)}{(x-5)} = \frac{96}{4} = 24
\]
So, the value of the expression \(\frac{(x+3)(x-1)}{(x-5)}\)[/tex] for [tex]\( x=9 \)[/tex] is [tex]\(\boxed{24}\)[/tex].
