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Simplify. Express your answer as a single fraction in simplest form. \newlinebc4−4b5\frac{bc}{4} - \frac{4b}{5}

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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. \newlinebc4−4b5\frac{bc}{4} - \frac{4b}{5}
  1. Identify LCD: Identify the least common denominator (LCD) for the fractions bc4\frac{bc}{4} and 4b5\frac{4b}{5}. The denominators are 44 and 55, so the LCD is their least common multiple, which is 2020.
  2. Rewrite fractions: Rewrite each fraction with the common denominator of 2020.bc4\frac{bc}{4} becomes bc×54×5=5bc20\frac{bc \times 5}{4 \times 5} = \frac{5bc}{20}.4b5\frac{4b}{5} becomes 4b×45×4=16b20\frac{4b \times 4}{5 \times 4} = \frac{16b}{20}.
  3. Subtract fractions: Subtract the two fractions with the common denominator.\newline(5bc20)−(16b20)=5bc−16b20(\frac{5bc}{20}) - (\frac{16b}{20}) = \frac{5bc - 16b}{20}.
  4. Factor out bb: Factor out the common factor bb from the numerator.\newline(5bc−16b)/20=b(5c−16)/20(5bc - 16b)/20 = b(5c - 16)/20.
  5. Check for simplification: Check if there are any common factors between the numerator and the denominator that can be simplified.\newlineThere are no common factors between b(5c−16)b(5c - 16) and 2020 that can be simplified, so the fraction is already in its simplest form.

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