(x^(3)+9x^(2))/(x^(3)) Which expression is equivalent to the given expression for all x > 1 ? Choose 1 answer: (A) 9x^(2) (B) 1+9x^(2) (C) (x+9)/(x) (D) (1+9x)/(x)

Simplify Expression: Simplify the given expression by dividing each term in the numerator by the term in the denominator. The expression is (x^(3)+9x^(2))/(x^(3)). We can divide each term in the numerator by x^(3) separately.Divide Terms: Divide x^(3) by x^(3) and 9x^(2) by x^(3). x^(3)/x^(3) = 1 (since any non-zero number divided by itself is 1) 9x^(2)/x^(3) = 9/x (since when dividing powers with the same base, we subtract the exponents: 2 - 3 = -1)Combine Results: Combine the results from Step 2. The simplified expression is 1 + 9/x.Match Answer Choices: Match the simplified expression with the given answer choices. The simplified expression 1 + 9/x corresponds to answer choice (D) (1+9x)/(x).

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Math Problems

Algebra 2

Simplify rational expressions

Full solution

\frac{x^{3}+9 x^{2}}{x^{3}}

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Which expression is equivalent to the given expression for all

x>1

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Choose

1

answer:

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(A)

9 x^{2}

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(B)

1+9 x^{2}

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(C)

\frac{x+9}{x}

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(D)

\frac{1+9 x}{x}

Simplify Expression: Simplify the given expression by dividing each term in the numerator by the term in the denominator. $\newline$ The expression is $(x^{3}+9x^{2})/(x^{3})$ . We can divide each term in the numerator by $x^{3}$ separately.
Divide Terms: Divide $x^{3}$ by $x^{3}$ and $9x^{2}$ by $x^{3}$ .
$x^{3}/x^{3} = 1$ (since any non-zero number divided by itself is $1$ )
$9x^{2}/x^{3} = 9/x$ (since when dividing powers with the same base, we subtract the exponents: $2 - 3 = -1$ )
Combine Results: Combine the results from Step $2$ . $\newline$ The simplified expression is $1 + \frac{9}{x}.$
Match Answer Choices: Match the simplified expression with the given answer choices. $\newline$ The simplified expression $1 + \frac{9}{x}$ corresponds to answer choice (D) $\left(1+9x\right)/\left(x\right)$ .