Question

Reducing the expression (a² - b² / ab) - (ab - b² / ab - a²) to the lowest terms, we get _____.

Answer 1

Dear student
$$\begin{gathered} \left(\frac{{\mathrm{a}}^2-{\mathrm{b}}^2}{\mathrm{ab}}\right)-\left(\frac{\mathrm{ab}-{\mathrm{b}}^2}{\mathrm{ab}-{\mathrm{a}}^2}\right) \\ \Rightarrow \left(\frac{{\mathrm{a}}^2-{\mathrm{b}}^2}{\mathrm{ab}}\right)-\frac{\mathrm{b}\left(\mathrm{a}-\mathrm{b}\right)}{\mathrm{a}\left(\mathrm{b}-\mathrm{a}\right)} \\ \Rightarrow \left(\frac{{\mathrm{a}}^2-{\mathrm{b}}^2}{\mathrm{ab}}\right)+\frac{\mathrm{b}}{\mathrm{a}} \\ \Rightarrow \frac{{\mathrm{a}}^2-{\mathrm{b}}^2+{\mathrm{b}}^2}{\mathrm{ab}} \\ \Rightarrow \frac{{\mathrm{a}}^2}{\mathrm{ab}} \\ \Rightarrow \frac{\mathrm{a}}{\mathrm{b}} \end{gathered}$$