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Simplify. Express your answer as a single fraction in simplest form. \newline4a+5a\frac{4}{a} + 5a

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline4a+5a\frac{4}{a} + 5a
  1. Identify Common Denominator: First, we need to identify the common denominator to combine the terms into a single fraction. Since one term is already a fraction with a denominator of aa, and the other term is a whole number, we can rewrite the whole number as a fraction with a denominator of aa by multiplying it by aa\frac{a}{a}.
  2. Rewrite Whole Number as Fraction: Now, let's rewrite the whole number 5a5a as a fraction:\newline5a=5a×aa5a = \frac{5a \times a}{a}\newlineThis gives us 5a2a\frac{5a^2}{a}.
  3. Combine Fractions: Next, we combine the two fractions over the common denominator aa: 4a+5a2a\frac{4}{a} + \frac{5a^2}{a}
  4. Add Numerators: Now, we add the numerators while keeping the common denominator: (4+5a2)/a(4 + 5a^2) / a
  5. Check for Simplification: Finally, we check if the numerator can be simplified further. Since 44 and 5a25a^2 have no common factors other than 11, the fraction is already in its simplest form.

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