Question

Simplify the following rational expression to determine if thegiven simplification is correct. If it is correct, select TRUE. If it isnot correct, select FALSE.3r217528r44

Answer 1

The expression given is,

`-(21r^5)/(28r^4)=-(3r)/(4)`

To prove if the left-hand side is equal to the right-hand side, we will reduce the left-hand side expression to its lowest term.

The left-hand side expression is,

`-(21r^5)/(28r^4)`

Factor the number 21 :

`\begin{gathered} 21=7*3 \\ =-(7*\: 3r^5)/(28r^4) \end{gathered}`

Factor the number 28:

`\begin{gathered} 28=7*4 \\ =-(7*\: 3r^5)/(7*\: 4r^4) \end{gathered}`

Cancel the common factor 7:

`=-(3r^5)/(4r^4)`

Simplify

`\begin{gathered} (r^5)/(r^4)(=r^4* r)/(r^4)=r \\ \therefore(r^5)/(r^4)=r \end{gathered}`

Therefore,

`-(3r^5)/(4r^4)=-(3r)/(4)`

Now comparing both the right-hand side and the left-hand side, we can see that both are the same.

Hence, the answer is TRUE.