Question

Divide the polynomial by the monomial denominator by writing the fraction as the sum (or difference) of fractions. Simplify your answer, if possible.Simplify your answer (- 5x + 10)/- 5

Answer 1

To answer this question, we have:

`(-5x+10)/(-5)`

This is equivalent to the following:

`(-5x)/(-5)+(10)/(-5)`

Then we have:

`\begin{gathered} (-5x)/(-5)=(5x)/(5) \\ (10)/(-5)=-(10)/(5) \end{gathered}`

Therefore, we have:

`(5x)/(5)-(10)/(5)`

If we simplify both fractions, we finally have:

`\begin{gathered} (5x)/(5)\Rightarrow(5)/(5)=1,(a)/(a)=1 \\ (5x)/(5)=1\cdot x=x \end{gathered}`

And

`-(10)/(5)=-2`

Then after simplification, we finally have:

`\begin{gathered} x-2 \\ \end{gathered}`

In summary, the process was as follows:

`\begin{gathered} (-5x+10)/(-5)=(-5x)/(-5)+(10)/(-5)=(-5)/(-5)x-(10)/(5)=(5x)/(5)-(10)/(5) \\ (5)/(5)x-(10)/(5)=x-2 \end{gathered}`

The final result is, then, x - 2.