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Answer :
Certainly! Let's simplify the expression [tex]\(\frac{28x^4 + 19x^3 + 36x^2}{4x^2}\)[/tex] step by step.
### Step-by-Step Solution:
1. Separate the Terms:
Our expression is a fraction where the numerator is [tex]\(28x^4 + 19x^3 + 36x^2\)[/tex] and the denominator is [tex]\(4x^2\)[/tex].
2. Divide Each Term by the Denominator:
We will divide each term in the numerator independently by [tex]\(4x^2\)[/tex].
- First Term:
[tex]\[
\frac{28x^4}{4x^2} = 7x^{4-2} = 7x^2
\][/tex]
- Second Term:
[tex]\[
\frac{19x^3}{4x^2} = \frac{19}{4}x^{3-2} = \frac{19}{4}x
\][/tex]
- Third Term:
[tex]\[
\frac{36x^2}{4x^2} = \frac{36}{4}x^{2-2} = 9
\][/tex]
3. Combine the Simplified Terms:
Putting all the simplified terms together gives us the final expression:
[tex]\[
7x^2 + \frac{19}{4}x + 9
\][/tex]
So, the simplified expression is [tex]\(7x^2 + \frac{19}{4}x + 9\)[/tex].
### Step-by-Step Solution:
1. Separate the Terms:
Our expression is a fraction where the numerator is [tex]\(28x^4 + 19x^3 + 36x^2\)[/tex] and the denominator is [tex]\(4x^2\)[/tex].
2. Divide Each Term by the Denominator:
We will divide each term in the numerator independently by [tex]\(4x^2\)[/tex].
- First Term:
[tex]\[
\frac{28x^4}{4x^2} = 7x^{4-2} = 7x^2
\][/tex]
- Second Term:
[tex]\[
\frac{19x^3}{4x^2} = \frac{19}{4}x^{3-2} = \frac{19}{4}x
\][/tex]
- Third Term:
[tex]\[
\frac{36x^2}{4x^2} = \frac{36}{4}x^{2-2} = 9
\][/tex]
3. Combine the Simplified Terms:
Putting all the simplified terms together gives us the final expression:
[tex]\[
7x^2 + \frac{19}{4}x + 9
\][/tex]
So, the simplified expression is [tex]\(7x^2 + \frac{19}{4}x + 9\)[/tex].
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