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Simplify. Express your answer as a single fraction in simplest form. \newline54−2r\frac{5}{4} - \frac{2}{r}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline54−2r\frac{5}{4} - \frac{2}{r}
  1. Identify LCD: 54−2r\frac{5}{4} - \frac{2}{r}\newlineIdentify the least common denominator (LCD) to combine the fractions.\newlineThe LCD for 44 and rr is 4r4r.
  2. Rewrite fractions: 54−2r\frac{5}{4} - \frac{2}{r}\newlineRewrite each fraction with the common denominator 4r4r.\newline(5⋅r4⋅r)−(2⋅4r⋅4)\left(\frac{5 \cdot r}{4 \cdot r}\right) - \left(\frac{2 \cdot 4}{r \cdot 4}\right)\newline=5r4r−84r=\frac{5r}{4r} - \frac{8}{4r}
  3. Combine fractions: (5r4r)−(84r)(\frac{5r}{4r}) - (\frac{8}{4r})\newlineCombine the fractions over the common denominator.\newline(5r−84r)(\frac{5r - 8}{4r})
  4. Check for simplification: 5r−84r\frac{5r - 8}{4r}\newlineCheck if the numerator and denominator have any common factors that can be simplified.\newlineThere are no common factors between 5r−85r - 8 and 4r4r, so the fraction is already in simplest form.

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