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Simplify. Express your answer as a single fraction in simplest form. \newlinebc25+b3\frac{bc^2}{5} + \frac{b}{3}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newlinebc25+b3\frac{bc^2}{5} + \frac{b}{3}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions.\newlineThe denominators are 55 and 33, so the LCD is 5×3=155 \times 3 = 15.
  2. Rewrite fractions: Rewrite each fraction with the common denominator of 1515.bc25\frac{bc^2}{5} becomes bc2×35×3\frac{bc^2 \times 3}{5 \times 3} which simplifies to 3bc215\frac{3bc^2}{15}.b3\frac{b}{3} becomes b×53×5\frac{b \times 5}{3 \times 5} which simplifies to 5b15\frac{5b}{15}.
  3. Add fractions: Add the fractions with the common denominator.\newline(3bc215)+(5b15)(\frac{3bc^2}{15}) + (\frac{5b}{15}) becomes (3bc2+5b15)(\frac{3bc^2 + 5b}{15}).
  4. Check numerator: Check if the numerator can be simplified.\newlineThe terms in the numerator 3bc23bc^2 and 5b5b do not have common factors other than bb, so the numerator cannot be simplified further.

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