Answer:
[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
Step-by-step explanation:
Given Parameters;
(m-4)/(m+4) and (m+2)
Required:
To divide and write out the equivalent expression.
Two or more expressions are said to equivalent if and only if they give the same result.
Solving (m-4)/(m+4) divided by (m+2)
We have
[tex]\frac{m - 4}{m + 4}[/tex] divided by [tex]m + 2[/tex]
[tex]= \frac{m - 4}{m + 4} / (m + 2)[/tex]
Convert division to multiplication
[tex]= \frac{m - 4}{m + 4} *\frac{1}{(m + 2)}[/tex]
= [tex]\frac{(m - 4) * 1}{(m + 4) * (m + 2)}[/tex]
[tex]= \frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
We can't simplify any further;
Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
To check if this is true
Let m = 1
[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] becomes
[tex]\frac{1 - 4}{1 + 4} / (1 + 2)[/tex]
[tex]\frac{-3}{5} / (3)[/tex]
[tex]\frac{-3}{5} * \frac{1}{3}[/tex]
[tex]\frac{-1}{5}[/tex]
And
[tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex] becomes
[tex]\frac{(1 - 4)}{(1 + 4)(1 + 2)}[/tex]
[tex]\frac{(-3)}{(5)(3)}[/tex]
[tex]\frac{-1}{5}[/tex]
Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
