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

Answer:

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

Step-by-step 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;

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

Cancel out the common factors to get:

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

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