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Simplify. Express your answer as a single fraction in simplest form. \newline37c+2b\frac{3}{7c} + \frac{2}{b}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline37c+2b\frac{3}{7c} + \frac{2}{b}
  1. Find LCM of denominators: Find the least common multiple (LCM) of the denominators 7c7c and bb. Since 7c7c and bb are different and we have no information that they have any common factors, the LCM is simply their product, 7bc7bc.
  2. Make denominators the same: Make the denominators the same by multiplying the first fraction by bb\frac{b}{b} and the second fraction by 7c7c\frac{7c}{7c}. This gives us 3b7bc+14c7bc\frac{3b}{7bc} + \frac{14c}{7bc}.
  3. Simplify the expression: Simplify the expression by adding the numerators since the denominators are the same. The final simplified expression is (3b+14c)/(7bc)(3b + 14c)/(7bc).

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