Question

Simplify (Y^2+7y+6)/(6y^2-6)

Answer 1

For this case we must simplify the following expression:

`\frac {y ^ 2 + 7y + 6} {6y ^ 2-6}`

We factor the numerator, looking for two numbers that when multiplied by 6 and when added together give 7. These numbers are +6 and +1.

Then, rewriting the expression:

`\frac {(y + 6) (y + 1)} {6 (y ^ 2-1)} =`

We rewrite the denominator:

`\frac {(y + 6) (y + 1)} {6 (y + 1) (y-1)} =`

We simplify similar terms:

`\frac {(y + 6)} {6 (y-1)}`

Answer:

`\frac {(y + 6)} {6 (y-1)}`

Answer 2

`(y + 6)/(6(y - 1))`

Explanation:

The given expression is

`\frac{ {y}^(2) + 7y + 6}{6 {y}^(2) - 6}`

The numerator is a quadratic trinomial and the denominator is different of two squares when 6 is factored.

We factor both the numerator and the denominator to obtain;

`( (y + 6)(y + 1) )/(6(y - 1)(y + 1))`

Cancel out the common factors to get:

`(y + 6)/(6(y - 1))`

This is the simplest form since, we cannot simplify this further.