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Simplify. Express your answer as a single fraction in simplest form. \newline5a+4b\frac{5}{a} + 4b

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline5a+4b\frac{5}{a} + 4b
  1. Identify Common Denominator: First, we need to identify the common denominator for the fractions. Since 4b4b is not a fraction, we can consider it as 4b1\frac{4b}{1}. The common denominator for the fractions 5a\frac{5}{a} and 4b1\frac{4b}{1} is aa.
  2. Rewrite Terms with Common Denominator: Now, we will rewrite each term with the common denominator aa. The first term is already in the correct form, 5a\frac{5}{a}. The second term, 4b4b, needs to be multiplied by aa\frac{a}{a} to have the common denominator.
  3. Combine Terms: After rewriting the second term, we have 4b×(a/a)4b \times (a/a) which is equal to (4ab)/a(4ab)/a. Now we can combine the two terms.
  4. Check for Further Simplification: Combining the two terms with the common denominator gives us (5+4ab)/a(5 + 4ab)/a. This is the expression simplified as a single fraction.
  5. Check for Further Simplification: Combining the two terms with the common denominator gives us (5+4ab)/a(5 + 4ab)/a. This is the expression simplified as a single fraction.Finally, we check if the fraction can be simplified further. Since 55 and 4ab4ab do not have common factors, and aa is already in the denominator, the fraction is in its simplest form.

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