Question

Write the following rational expression in lowest term

Answer 1

Given rational expression is

`(t^2-4)/(6t-12)`

Factor the numerator and denominator first.

`\begin{gathered} t^2-4=t^2-2^2 \\ =(t+2)(t-2) \end{gathered}`

Factor the denominator 6t-12:

`\begin{gathered} 6t-12=6t-6\cdot2 \\ =6(t-2) \end{gathered}`

So,

`\begin{gathered} (t^2-4)/(6t-12)=((t+2)(t-2))/(6(t-2)) \\ =(t+2)/(6) \end{gathered}`

Therefore, the given expression in lowest form is

`(t+2)/(6)`