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:

$\frac{-5x+10}{-5}$

This is equivalent to the following:

$\frac{-5x}{-5}+\frac{10}{-5}$

Then we have:

$\begin{gathered} \frac{-5x}{-5}=\frac{5x}{5} \\ \frac{10}{-5}=-\frac{10}{5} \end{gathered}$

Therefore, we have:

$\frac{5x}{5}-\frac{10}{5}$

If we simplify both fractions, we finally have:

$\begin{gathered} \frac{5x}{5}\Rightarrow\frac{5}{5}=1,\frac{a}{a}=1 \\ \frac{5x}{5}=1\cdot x=x \end{gathered}$

And

$-\frac{10}{5}=-2$

Then after simplification, we finally have:

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

In summary, the process was as follows:

$\begin{gathered} \frac{-5x+10}{-5}=\frac{-5x}{-5}+\frac{10}{-5}=\frac{-5}{-5}x-\frac{10}{5}=\frac{5x}{5}-\frac{10}{5} \\ \frac{5}{5}x-\frac{10}{5}=x-2 \end{gathered}$

The final result is, then, x - 2.