How do you multiply (3y^2+18y+15)/(6y+6)*(y-5)/(y^2-25)?

1 Answer
Aug 18, 2016

(3y^2 + 18y + 15)/(6y + 6) xx (y - 5)/(y^2 - 25) =color(green)( 1/2, y != -5, -1, 5)

Explanation:

For problems like these, you must start by factoring everything.

3y^2 + 18y + 5 can be factored as:

3(y^2 + 6y + 5) = 3(y + 5)(y + 1)

6y + 6 can be factored as:

6(y + 1)

y - 5 is as simplified as it can be.

y^2 - 25 can be factored as (y + 5)(y - 5)

Putting all of this back together:

(3(y + 5)(y + 1))/(6(y + 1)) xx (y - 5)/((y + 5)(y - 5))

See what you can cancel out, using the property a/a = 1:

(cancel((3))cancel((y + 5))cancel((y + 1)))/(cancel((6))^2cancel((y + 1))) xx (cancel(y - 5))/(cancel((y + 5))cancel((y - 5)))

We are left with:

1/2

Now, before stating the final answer, we need to determine any restrictions on the variable. These will occur when the denominator equals 0. Hence, they can be found by setting the denominator to 0 and solving for x.

6y + 6 = 0" and "y^2 - 25 = 0

y = -1 " and "y = +-5

Thus, y != -1, 5, -5

Hopefully this helps!