What is the value of n for the equation?

Question

asked Oct 10, 2023 6.1k views

1 Answer

Pankaj Prakash · Answer 1 · 2023-10-17T10:40:41+0000

Answer:

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

$\Rightarrow \sf n=-10$