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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{5}{4} - \frac{5}{7u^4v}$

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Add and subtract rational expressions

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{5}{4} - \frac{5}{7u^4v}

Find LCM of Denominators: Find the least common multiple (LCM) of the denominators $4$ and $7u^4v$ . Since $4$ and $7$ are coprime and do not share any factors with $u^4v$ , the LCM is simply $4 \times 7u^4v$ , which is $28u^4v$ .
Make Denominators Same: Make the denominators the same by multiplying the first fraction by $7u^4v$ and the second fraction by $4$ . This gives us $(5 \times 7u^4v)/28u^4v - (5 \times 4)/28u^4v$ .
Perform Numerator Multiplication: Perform the multiplication for both numerators. This results in $(35u^4v)/28u^4v - \frac{20}{28u^4v}$ .
Simplify Expression: Simplify the expression by subtracting the numerators since the denominators are the same. The final simplified expression is $(35u^4v - 20)/28u^4v$ .
Check for Further Simplification: Check if the numerator can be simplified further. In this case, there are no common factors between $35u^4v$ and $20$ , so the fraction is already in its simplest form.

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