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Simplify. Express your answer as a single fraction in simplest form. \newline54−57u4v\frac{5}{4} - \frac{5}{7u^4v}

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Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline54−57u4v\frac{5}{4} - \frac{5}{7u^4v}
  1. Find LCM of Denominators: Find the least common multiple (LCM) of the denominators 44 and 7u4v7u^4v. Since 44 and 77 are coprime and do not share any factors with u4vu^4v, the LCM is simply 4×7u4v4 \times 7u^4v, which is 28u4v28u^4v.
  2. Make Denominators Same: Make the denominators the same by multiplying the first fraction by 7u4v7u^4v and the second fraction by 44. This gives us (5×7u4v)/28u4v−(5×4)/28u4v(5 \times 7u^4v)/28u^4v - (5 \times 4)/28u^4v.
  3. Perform Numerator Multiplication: Perform the multiplication for both numerators. This results in (35u4v)/28u4v−2028u4v(35u^4v)/28u^4v - \frac{20}{28u^4v}.
  4. Simplify Expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is (35u4v−20)/28u4v(35u^4v - 20)/28u^4v.
  5. Check for Further Simplification: Check if the numerator can be simplified further. In this case, there are no common factors between 35u4v35u^4v and 2020, so the fraction is already in its simplest form.

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