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Simplify. Express your answer as a single fraction in simplest form. \newline54c2b3\frac{5}{4c} - \frac{2b}{3}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline54c2b3\frac{5}{4c} - \frac{2b}{3}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions.\newlineThe denominators are 4c4c and 33. The LCD for these two denominators is 12c12c because 12c12c is the smallest number that both 4c4c and 33 will divide into without a remainder.
  2. Rewrite fractions: Rewrite each fraction with the common denominator of 12c12c. To convert the first fraction, 54c\frac{5}{4c}, to have a denominator of 12c12c, multiply both the numerator and the denominator by 33. For the second fraction, 2b3\frac{2b}{3}, multiply both the numerator and the denominator by 4c4c. (54c)(33)=1512c(\frac{5}{4c}) \cdot (\frac{3}{3}) = \frac{15}{12c} (2b3)(4c4c)=8bc12c(\frac{2b}{3}) \cdot (\frac{4c}{4c}) = \frac{8bc}{12c}
  3. Combine fractions: Combine the fractions with the common denominator.\newlineNow that both fractions have the same denominator, you can combine them by subtracting the numerators and keeping the common denominator.\newline(1512c)(8bc12c)=158bc12c(\frac{15}{12c}) - (\frac{8bc}{12c}) = \frac{15 - 8bc}{12c}
  4. Simplify expression: Simplify the expression, if possible.\newlineIn this case, the numerator 158bc15 - 8bc cannot be simplified further because there are no common factors between the terms. Therefore, the expression in simplest form is 158bc12c\frac{15 - 8bc}{12c}.

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