To simplify the given mathematical expression:
[tex]\[
\frac{4 + 7x}{(2 + 3x)(1 + x)^2}
\][/tex]
Let's go through the process step-by-step.
1. Original Expression:
[tex]\[
\frac{4 + 7x}{(2 + 3x)(1 + x)^2}
\][/tex]
2. Rewrite the denominator to keep it in factor form for simplicity:
The denominator is already factored as [tex]\((2 + 3x)(1 + x)^2\)[/tex].
3. Combine the expressions into a single fraction:
This step is already done in the initial expression; nothing changes here.
4. Observe any common factors:
There's no common factor between the numerator [tex]\(4+7x\)[/tex] and the denominator [tex]\((2 + 3x)(1 + x)^2\)[/tex] that can be directly canceled.
Thus, the simplified form of the expression remains:
[tex]\[
\frac{7x + 4}{(x + 1)^2 \cdot (3x + 2)}
\][/tex]
So, the simplified mathematical expression is:
[tex]\[
\frac{7x + 4}{(x + 1)^2 \cdot (3x + 2)}
\][/tex]
This is the final simplified form.
