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Simplify. Express your answer as a single fraction in simplest form. \newline14−49rs\frac{1}{4} - \frac{4}{9rs}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline14−49rs\frac{1}{4} - \frac{4}{9rs}
  1. Identify Common Denominator: Identify the common denominator for the fractions 14\frac{1}{4} and 49rs\frac{4}{9\text{rs}}.\newlineSince the denominators 44 and 9rs9\text{rs} have no common factors, the common denominator will be their product, which is 36rs36\text{rs}.
  2. Rewrite Fractions: Rewrite each fraction with the common denominator.\newlineFor the first fraction, multiply both the numerator and denominator of 14\frac{1}{4} by 9rs9rs to get (1×9rs4×9rs)=9rs36rs\left(\frac{1\times 9rs}{4\times 9rs}\right) = \frac{9rs}{36rs}.\newlineFor the second fraction, multiply both the numerator and denominator of 49rs\frac{4}{9rs} by 44 to get (4×49rs×4)=1636rs\left(\frac{4\times 4}{9rs\times 4}\right) = \frac{16}{36rs}.
  3. Combine Fractions: Combine the fractions over the common denominator.\newlineNow we have (9rs36rs)−(1636rs)=9rs−1636rs(\frac{9rs}{36rs}) - (\frac{16}{36rs}) = \frac{9rs - 16}{36rs}.
  4. Simplify Expression: Simplify the expression if possible.\newlineIn this case, the numerator 9rs−169rs - 16 cannot be simplified further, and the denominator 36rs36rs is already in simplest form. Therefore, the expression is already in its simplest form.

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