Question

subtract. state the difference in simplest form.
\\(\frac{9}{4m} - \frac{4}{9n}\\)
\\(\circ\\) \\(\frac{m - n}{mn}\\)
\\(\circ\\) \\(\frac{5}{4m - 9n}\\)
\\(\circ\\) \\(\frac{5}{36mn}\\)
\\(\circ\\) \\(\frac{81n - 16m}{36mn}\\)

Explanation:

Step1: Find the common denominator

The denominators are \(4m\) and \(9n\). The least common denominator (LCD) of \(4m\) and \(9n\) is \(36mn\) (since \(4\) and \(9\) have a least common multiple of \(36\), and we include the variables \(m\) and \(n\)).

Step2: Rewrite fractions with LCD

Rewrite \(\frac{9}{4m}\) and \(\frac{4}{9n}\) with the denominator \(36mn\):

• For \(\frac{9}{4m}\), multiply numerator and denominator by \(9n\): \(\frac{9\times9n}{4m\times9n}=\frac{81n}{36mn}\)
• For \(\frac{4}{9n}\), multiply numerator and denominator by \(4m\): \(\frac{4\times4m}{9n\times4m}=\frac{16m}{36mn}\)

Step3: Subtract the fractions

Now subtract the two fractions: \(\frac{81n}{36mn}-\frac{16m}{36mn}=\frac{81n - 16m}{36mn}\)

Answer:

\(\frac{81n - 16m}{36mn}\) (the last option: \(\boldsymbol{\frac{81n - 16m}{36mn}}\))