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Simplify. Express your answer as a single fraction in simplest form. \newline9b25bc\frac{9b}{2} - \frac{5}{bc}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline9b25bc\frac{9b}{2} - \frac{5}{bc}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions.\newlineThe fractions are 9b2\frac{9b}{2} and 5bc\frac{5}{bc}. The LCD for these fractions is 2bc2bc because it is the smallest number that both denominators (22 and bcbc) will divide into without a remainder.
  2. Rewrite fractions: Rewrite each fraction with the common denominator.\newlineTo rewrite 9b2\frac{9b}{2} with the common denominator, multiply both the numerator and the denominator by cc to get (9bc)(2c)\frac{(9b \cdot c)}{(2 \cdot c)}. To rewrite 5bc\frac{5}{bc} with the common denominator, multiply both the numerator and the denominator by 22 to get (52)(bc2)\frac{(5 \cdot 2)}{(bc \cdot 2)}.
  3. Perform multiplication: Perform the multiplication from Step 22.\newlineFor the first fraction, (9b×c)/(2×c)(9b \times c)/(2 \times c) simplifies to 9bc/2bc9bc/2bc. For the second fraction, (5×2)/(bc×2)(5 \times 2)/(bc \times 2) simplifies to 10/2bc10/2bc.
  4. Combine fractions: Combine the fractions over the common denominator.\newlineNow that both fractions have the common denominator of 2bc2bc, we can combine them into a single fraction:\newline9bc2bc102bc=9bc102bc\frac{9bc}{2bc} - \frac{10}{2bc} = \frac{9bc - 10}{2bc}
  5. Simplify numerator: Simplify the numerator if possible.\newlineIn this case, the numerator 9bc109bc - 10 cannot be simplified further because there are no common factors between 9bc9bc and 1010.
  6. Check for simplification: Check if the fraction can be simplified further.\newlineThe fraction (9bc10)/2bc(9bc - 10)/2bc is already in simplest form because the numerator and the denominator have no common factors other than 11.

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