Question

Simplify the rational expression: 6n^2+8n+2/2n^2-2

Answer 1

To simplify the given rational expression, factor both the numerator and the denominator, cancel common factors, and ensure the remaining terms do not simplify further to obtain the simplified form.

To simplify the rational expression
`6n^2`+8n+2 over
`2n^2`-2, we first look at the numerator and denominator to determine if they can be factored. The numerator factors as 2(
`3n^2`+4n+1). The denominator can be written as 2(
`n^2`-1), which is a difference of squares and can be factored further into 2(n+1)(n-1).

After factoring, our expression is (2(
`3n^2`+4n+1)) / (2(n+1)(n-1)). We can eliminate terms by cancelling out the common factor of 2, leaving us with (
`3n^2`+4n+1) / ((n+1)(n-1)). However, the numerator does not simplify further with the denominator, so this is the simplified form of the expression.

It's always important to check the answer to ensure that it is reasonable and that no additional simplification can be done.