Question
9. Simplify the following expression, for \( x \neq 0 \) \( \frac{9 x^{3}+4 x^{2}}{x} \) \( \frac{9 x^{3}+4 x^{2}}{x}= \) Enter your next step here
Ask by Zimmerman Hobbs. in the United States
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 9x^2 + 4x \)
Solution
Step 1: Factor the numerator by extracting the common factor \( x \):
\[
9x^3 + 4x^2 = x(9x^2 + 4x)
\]
Step 2: Substitute back into the fraction:
\[
\frac{9x^3 + 4x^2}{x} = \frac{x(9x^2 + 4x)}{x}
\]
Step 3: Cancel the common factor \( x \) (since \( x \neq 0 \)):
\[
\frac{x(9x^2 + 4x)}{x} = 9x^2 + 4x
\]
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Simplify this solution Extra Insights
To simplify the expression \( \frac{9 x^{3}+4 x^{2}}{x} \), you can factor out the \( x \) from the numerator. This gives you \( \frac{x(9x^{2}+4x)}{x} \). Since \( x \neq 0 \), you can safely cancel the \( x \) in the numerator and the denominator, leading to \( 9x^{2}+4x \). Next, you can further factor the resulting expression \( 9x^{2}+4x \). Factoring \( x \) out gives you \( x(9x + 4) \). So, the finalized simplified version is \( x(9x + 4) \). This shows how polynomial expressions can often be simplified through factoring techniques!
