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Simplify. Express your answer as a single fraction in simplest form. \newline2a+1\frac{2}{a} + 1

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline2a+1\frac{2}{a} + 1
  1. Identify Expression: Identify the expression to be simplified.\newlineWe have the expression 2a+1\frac{2}{a} + 1. To combine these terms into a single fraction, we need a common denominator.
  2. Find Common Denominator: Find a common denominator.\newlineThe common denominator for 2a\frac{2}{a} and 11 is aa, since 11 can be written as aa\frac{a}{a}.
  3. Rewrite as a/aa/a: Rewrite 11 as a/aa/a. We can express 11 as a/aa/a so that both terms have the same denominator. 1=a/a1 = a/a
  4. Combine Fractions: Combine the fractions.\newlineNow that we have a common denominator, we can combine the fractions.\newline2a+aa=2+aa\frac{2}{a} + \frac{a}{a} = \frac{2 + a}{a}
  5. Check for Simplification: Check for any possible simplification.\newlineThe fraction (2+a)/a(2 + a)/a is already in simplest form because the numerator and the denominator have no common factors other than 11.

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