Simplify this expression? (5y^2-10y)/(y^2-y-6)?

Question

Simplify the expression:

(5y^2-10y)/(y^2-y-6) =

Show your work... I really need help with this, I have a whole sheet with these, and need someone to help explain what I need to do!

Thanks!

I copied the problem wrong...

(5y^2-10y)/(y^2+y-6)

Answer 1

5 y ( y - 2 )
-----------------
( y + 3 ) ( y - 2 )

5 y
-------
( y + 3 )

Answer 2

When you are asked to simplify a rational function such as this one, it is always good to look at the numerator and denominator separately.

** numerator *** 5y² - 10y

What is common between these two terms? y, obviously, and in fact, 5 as well, there is a 5 inside 10. Therefore we can factor those two out and get

5y(y-2)

** denominator ** y²+y-6 (after correcting for typo)

Try to factor this into (y+a)(y+b). Ask yourself, what two numbers (a and b) multiply to give -6 and and add to give +1? The answer is 3 and -2. Therefore you can factor the denominator into

(y+3)(y-2)

** Put them back together **

Now you should have

5y(y-2)
-----------
(y+3)(y-2)

The term y-2 can thus be canceled and you get 5y/(y+3).

Therefore, this type of question can be essentially answered with a 3 step process:
(1) factor the numerator
(2) factor the denominator
(3) cancel common factors (if any)

Now try it on the rest of your practice problems

Answer 3

Well this is how i would do it, although I think you copied the problem wrong!!!

(5y(y-2)) / (y+2)(y-3)

Nothing cancels because it should be (5y^2 +10y)/(y^2-y-6) or (5y^2-10y)/(y^2 + y-6). Hope I helped.

Answer 4

(5y^2-10y)/(y^2-y-6)

= (5y ( y-2)) / ((y-3)(y+2))

This is goign no where, are you sure it's not :

(5y^2 + 10y)/(y^2-y-6)


Like guy said above, DOH !


(5y^2-10y)/(y^2-y-6)