Let's simplify the given expression step-by-step:
The initial expression is:
[tex]\[
\frac{13x - 60}{8x + 32}
\][/tex]
Step 1: Identify common factors in the numerator and the denominator.
Notice that in the denominator, [tex]\(8x + 32\)[/tex] can be factored by factoring out a common multiple:
[tex]\[
8x + 32 = 8(x + 4)
\][/tex]
So the denominator becomes:
[tex]\[
8(x + 4)
\][/tex]
Step 2: Replace the denominator in the fraction:
[tex]\[
\frac{13x - 60}{8(x + 4)}
\][/tex]
Step 3: Inspect the numerator [tex]\(13x - 60\)[/tex] for any common factors with the denominator. In this case, there are no common factors between [tex]\(13x - 60\)[/tex] and [tex]\(8(x + 4)\)[/tex].
Since there are no further simplifications to perform, the expression in its simplified form is:
[tex]\[
\frac{13x - 60}{8(x + 4)}
\][/tex]
Thus, the final simplified form of the expression [tex]\(\frac{13x - 60}{8x + 32}\)[/tex] is:
[tex]\[
\frac{13x - 60}{8(x + 4)}
\][/tex]
