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x3+9x2x3\frac{x^3+9x^2}{x^3} which expression is equivalent to the given expression for all x>1?\newline(A) 9x29x^2\newline(B) 1+9x21+9x^2\newline(C) x+9xx+\frac{9}{x}\newline(D) 1+9xx1+\frac{9x}{x}

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Q. x3+9x2x3\frac{x^3+9x^2}{x^3} which expression is equivalent to the given expression for all x>1x>1?\newline(A) 9x29x^2\newline(B) 1+9x21+9x^2\newline(C) x+9xx+\frac{9}{x}\newline(D) 1+9xx1+\frac{9x}{x}
  1. Simplify Expression: Simplify the given expression by dividing each term in the numerator by the term in the denominator.\newlineThe expression is (x3+9x2)/(x3)(x^3+9x^2)/(x^3). We can divide each term in the numerator by x3x^3.\newlinex3/x3=1x^3/x^3 = 1\newline9x2/x3=9/x9x^2/x^3 = 9/x\newlineSo, the simplified expression is 1+9/x1 + 9/x.
  2. Match with Options: Match the simplified expression with the given options.\newlineThe simplified expression is 1+9x1 + \frac{9}{x}. Now we need to see which of the given options matches this expression.\newlineOption a) 9x29x^2 does not match because it does not have the term 11.\newlineOption b) 1+9x21+9x^2 does not match because it has x2x^2 instead of 1x\frac{1}{x}.\newlineOption c) x+9xx+\frac{9}{x} does not match because it has xx instead of 11.\newlineOption d) 1+9x1+\frac{9}{x} matches exactly with our simplified expression.

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