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Simplify. Express your answer as a single fraction in simplest form. \newline9a2+a5b4\frac{9a}{2} + \frac{a^5b}{4}

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Add and subtract rational expressionsright chevron icon

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline9a2+a5b4\frac{9a}{2} + \frac{a^5b}{4}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions.\newlineThe denominators are 22 and 44. The LCD for these two fractions is 44 because 44 is the smallest number that both 22 and 44 can divide into without leaving a remainder.
  2. Rewrite fraction: Rewrite the first fraction with the common denominator.\newlineTo convert the first fraction's denominator from 22 to 44, we multiply both the numerator and the denominator by 22.\newline(9a2)⋅(22)=18a4(\frac{9a}{2}) \cdot (\frac{2}{2}) = \frac{18a}{4}
  3. Combine fractions: Combine the fractions with the common denominator.\newlineNow that both fractions have the same denominator, we can combine them.\newline18a4+a5b4\frac{18a}{4} + \frac{a^5b}{4}
  4. Add numerators: Add the numerators of the fractions.\newlineSince the denominators are the same, we can add the numerators directly.\newline(18a+a5b)/4(18a + a^5b) / 4
  5. Check for simplification: Check if the expression can be simplified further.\newlineThe expression (18a+a5b)/4(18a + a^5b) / 4 is already in its simplest form because the numerator does not have any common factors with the denominator.

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