Question

Express the following as a simple fraction involving positive exponents only

Answer 1

Recall that if x≠0, then:

$\begin{gathered} x^{-m}=\frac{1}{x^m} \\ \text{where m is an integer.} \end{gathered}$

Therefore:

$2x^{-1}-5x^{-2}=\frac{2}{x}-\frac{5}{x^2}\text{.}$

Now, if x≠0, notice that:

$\frac{2}{x}=\frac{2x}{x^2}\text{.}$

Then:

$\begin{gathered} 2x^{-1}-5x^{-2}=\frac{2x}{x^2}-\frac{5}{x^2} \\ =\frac{2x-5}{x^2}\text{.} \end{gathered}$

Answer:

$\frac{2x-5}{x^2}\text{.}$