Solve 1/n-5-n-1/n^2+n-30=1/n+6

$$\frac{ 1 }{ n-5 } - \frac{ n-1 }{ { n }^{ 2 } +n-30 } = \frac{ 1 }{ n+6 }$$

Solve for n

$$n=12$$

Steps for Solving Linear Equation

Variable n cannot be equal to any of the values -6,5 since division by zero is not defined. Multiply both sides of the equation by \left(n-5\right)\left(n+6\right), the least common multiple of n-5,n^{2}+n-30,n+6.

$$n+6-\left(n-1\right)=n-5$$

To find the opposite of n-1, find the opposite of each term.

$$n+6-n+1=n-5$$

Combine n and -n to get 0.

$$6+1=n-5$$

Add 6 and 1 to get 7.

$$7=n-5$$

Swap sides so that all variable terms are on the left hand side.

$$n-5=7$$

Add 5 to both sides.

$$n=7+5$$

Add 7 and 5 to get 12.

$$n=12$$