Solve n+2/n^3-4n^2+1/n=n-5/n^2-4n

$$\frac { n + 2 } { n ^ { 3 } - 4 n ^ { 2 } } + \frac { 1 } { n } = \frac { n - 5 } { n ^ { 2 } - 4 n }$$

Solve for n

$$n=-1$$

Steps for Solving Linear Equation

Variable n cannot be equal to any of the values 0,4 since division by zero is not defined. Multiply both sides of the equation by \left(n-4\right)n^{2}, the least common multiple of n^{3}-4n^{2},n,n^{2}-4n.

$$n+2+\left(n-4\right)n=n\left(n-5\right)$$

Use the distributive property to multiply n-4 by n.

$$n+2+n^{2}-4n=n\left(n-5\right)$$

Combine n and -4n to get -3n.

$$-3n+2+n^{2}=n\left(n-5\right)$$

Use the distributive property to multiply n by n-5.

$$-3n+2+n^{2}=n^{2}-5n$$

Subtract n^{2} from both sides.

$$-3n+2+n^{2}-n^{2}=-5n$$

Combine n^{2} and -n^{2} to get 0.

$$-3n+2=-5n$$

Add 5n to both sides.

$$-3n+2+5n=0$$

Combine -3n and 5n to get 2n.

$$2n+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$2n=-2$$

Divide both sides by 2.

$$n=\frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$n=-1$$