Question

What is the value of n for the equation?

Answer 1

Answer:

n = -10

Explanation:

$\Rightarrow \sf \dfrac{1}{n} +\dfrac{4n+16}{n^2-6n} =\dfrac{4}{n-6}$

Factor the common term

$\Rightarrow \sf \dfrac{1}{n} +\dfrac{4n+16}{n(n-6)} =\dfrac{4}{n-6}$

Make the denominator same

$\Rightarrow \sf \dfrac{n-6}{n(n-6)} +\dfrac{4n+16}{n(n-6)} =\dfrac{4}{n-6}$

Join the fractions

$\Rightarrow \sf \dfrac{n-6+4n+16}{n(n-6)}=\dfrac{4}{n-6}$

simplify the following

$\Rightarrow \sf \dfrac{5n+10}{n(n-6)}=\dfrac{4}{n-6}$

cross multiply

$\Rightarrow \sf\left(5n+10\right)\left(n-6\right)=n\left(n-6\right)\cdot \:4$

cancel out common term

$\Rightarrow \sf\left(5n+10\right)=4n$

exchange sides

$\Rightarrow \sf 5n-4n=-10$

simplify

$\Rightarrow \sf n=-10$