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Simplify. Express your answer as a single fraction in simplest form. \newline3a2+b\frac{3}{a^2} + b

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline3a2+b\frac{3}{a^2} + b
  1. Identify Expression: Identify the expression to be simplified.\newlineWe have the expression 3a2+b\frac{3}{a^2} + b. To simplify this expression and write it as a single fraction, we need to combine the terms into a single denominator.
  2. Find Common Denominator: Find a common denominator.\newlineSince a2a^2 is already a denominator for the first term, and the second term bb is not a fraction, we can treat bb as b/1b/1. The common denominator for a2a^2 and 11 is a2a^2.
  3. Rewrite with Common Denominator: Rewrite both terms with the common denominator.\newlineWe rewrite bb as b×a2a2b\times\frac{a^2}{a^2} to have the same denominator as the first term.\newlineSo, the expression becomes 3a2+b×a2a2\frac{3}{a^2} + \frac{b\times a^2}{a^2}.
  4. Combine Over Common Denominator: Combine the terms over the common denominator.\newlineNow that both terms have the same denominator, we can combine them into a single fraction:\newline(3+ba2)/a2(3 + b\cdot a^2)/a^2.
  5. Check for Simplification: Check if the numerator can be simplified.\newlineThe numerator 3+bimesa23 + b imes a^2 does not have any common factors with the denominator a2a^2, and there are no like terms to combine in the numerator. Therefore, the expression is already in its simplest form.

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