Question

How do you simplify `\frac { 5} { n } - \frac { 6} { n ^ { 3} - 2n ^ { 2} } = \frac { n ^ { 2} + 5n - 6} { n ^ { 3} - 2n ^ { 2} }`?

Answer 1

`n=15/4`

Explanation:

Given
`color(white)("XXX")5/n-6/(n^3-2n^2)=(n^2+5n-6)/(n^3-2n^2)`

Multiplying everything on both sides by `(n^3-2n^2)=n(n^2-2n)`
`color(white)("XXX")5(n^2-2n)cancel(-6)=n^2+5ncancel(-6)`

`color(white)("XXX")5n^2-10n=n^2+5n`

`color(white)("XXX")4n^2-15n=0`

`color(white)("XXX")n(4n-15)=0`

`color(white)("XXX")n=0 or n=15/4`

Since the given equation is meaningless is `n=0` (attempting to divide by `0`) we can treat that result as extraneous.