Answer:
n = -10
Explanation:
[tex]\Rightarrow \sf \dfrac{1}{n} +\dfrac{4n+16}{n^2-6n} =\dfrac{4}{n-6}[/tex]
Factor the common term
[tex]\Rightarrow \sf \dfrac{1}{n} +\dfrac{4n+16}{n(n-6)} =\dfrac{4}{n-6}[/tex]
Make the denominator same
[tex]\Rightarrow \sf \dfrac{n-6}{n(n-6)} +\dfrac{4n+16}{n(n-6)} =\dfrac{4}{n-6}[/tex]
Join the fractions
[tex]\Rightarrow \sf \dfrac{n-6+4n+16}{n(n-6)}=\dfrac{4}{n-6}[/tex]
simplify the following
[tex]\Rightarrow \sf \dfrac{5n+10}{n(n-6)}=\dfrac{4}{n-6}[/tex]
cross multiply
[tex]\Rightarrow \sf\left(5n+10\right)\left(n-6\right)=n\left(n-6\right)\cdot \:4[/tex]
cancel out common term
[tex]\Rightarrow \sf\left(5n+10\right)=4n[/tex]
exchange sides
[tex]\Rightarrow \sf 5n-4n=-10[/tex]
simplify
[tex]\Rightarrow \sf n=-10[/tex]
