Question

Express the following as a simple fraction involving positive exponents only

Answer 1

Recall that if x≠0, then:

`\begin{gathered} x^(-m)=(1)/(x^m) \\ \text{where m is an integer.} \end{gathered}`

Therefore:

`2x^(-1)-5x^(-2)=(2)/(x)-(5)/(x^2)\text{.}`

Now, if x≠0, notice that:

`(2)/(x)=(2x)/(x^2)\text{.}`

Then:

`\begin{gathered} 2x^(-1)-5x^(-2)=(2x)/(x^2)-(5)/(x^2) \\ =(2x-5)/(x^2)\text{.} \end{gathered}`

Answer:

`(2x-5)/(x^2)\text{.}`