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Simplify. Express your answer as a single fraction in simplest form. \newline37rs−5r\frac{3}{7rs} - \frac{5}{r}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline37rs−5r\frac{3}{7rs} - \frac{5}{r}
  1. Identify common denominator: Identify the common denominator.\newlineTo combine the fractions, we need a common denominator. The least common denominator (LCD) for 7rs7rs and rr is 7rs7rs.
  2. Rewrite first fraction: Rewrite the first fraction with the common denominator.\newlineThe first fraction is already over the common denominator, so it remains unchanged.\newline37rs\frac{3}{7rs}
  3. Rewrite second fraction: Rewrite the second fraction with the common denominator.\newlineTo get the common denominator of 7rs7rs for the second fraction, we multiply both the numerator and the denominator by 7s7s.\newline5r×7s7s=35s7rs\frac{5}{r} \times \frac{7s}{7s} = \frac{35s}{7rs}
  4. Combine fractions: Combine the fractions.\newlineNow that both fractions have the common denominator, we can combine them.\newline37rs−35s7rs\frac{3}{7rs} - \frac{35s}{7rs}
  5. Subtract numerators: Subtract the numerators.\newlineSubtract the numerators while keeping the common denominator.\newline(3−35s)/7rs(3 - 35s)/7rs
  6. Simplify numerator: Simplify the numerator. Simplify the expression in the numerator. 3−35s3 - 35s cannot be simplified further because there are no like terms.

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