Question

What is the value of n for the equation?

Answer 1

n = -10

Step-by-step explanation:

`\Rightarrow \sf (1)/(n) +(4n+16)/(n^2-6n) =(4)/(n-6)`

Factor the common term

`\Rightarrow \sf (1)/(n) +(4n+16)/(n(n-6)) =(4)/(n-6)`

Make the denominator same

`\Rightarrow \sf (n-6)/(n(n-6)) +(4n+16)/(n(n-6)) =(4)/(n-6)`

Join the fractions

`\Rightarrow \sf (n-6+4n+16)/(n(n-6))=(4)/(n-6)`

simplify the following

`\Rightarrow \sf (5n+10)/(n(n-6))=(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`