Question

subtract.
\\(\frac{7}{2y^2} - \frac{2}{5y^3}\\)
simplify your answer as much as possible.

Explanation:

Step1: Find the common denominator

The denominators are \(2y^2\) and \(5y^3\). The least common denominator (LCD) is \(10y^3\) (since \(10\) is the LCM of \(2\) and \(5\), and \(y^3\) is the highest power of \(y\) present).

Step2: Rewrite fractions with LCD

Rewrite \(\frac{7}{2y^2}\) with denominator \(10y^3\): multiply numerator and denominator by \(5y\), so \(\frac{7\times5y}{2y^2\times5y}=\frac{35y}{10y^3}\).
Rewrite \(\frac{2}{5y^3}\) with denominator \(10y^3\): multiply numerator and denominator by \(2\), so \(\frac{2\times2}{5y^3\times2}=\frac{4}{10y^3}\).

Step3: Subtract the fractions

Now subtract the two fractions: \(\frac{35y}{10y^3}-\frac{4}{10y^3}=\frac{35y - 4}{10y^3}\).

Answer:

\(\frac{35y - 4}{10y^3}\)