# After I simplify 3y-15 / 3y+15, how to check I'm right?

#### ebrushman

##### New member
After I simplify this, is there a check to know I'm right?

3y-15 / 3y+15

#### tkhunny

##### Moderator
Staff member
The first thing to know is what the question is.

If you are simplifying, you may wish to notice the rampant remaining factor of 3.

#### ebrushman

##### New member
sorry
Simplify by removing factors of 1

#### galactus

##### Super Moderator
Staff member
Factor out 3 and cancel.

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

#### Subhotosh Khan

##### Super Moderator
Staff member
ebrushman said:
After I simplify this, is there a check to know I'm right?

3y-15 / 3y+15
As far as I know, there is NO definite check for that!

#### stapel

##### Super Moderator
Staff member
ebrushman said:
After I simplify [3y-15 / 3y+15], is there a check to know I'm right?
Subhotosh Khan said:
As far as I know, there is NO definite check for that!
You can sort of cheat with a graphing calculator: Graph the original expression as "Y1", and, on the same screen, graph your final expression as "Y2". If the two lines are the same, then you probably did the simplification correctly. :wink:

Eliz.

#### Denis

##### Senior Member
(3y - 15) / (3y + 15)
Assign a "nice" value to y, like 10:
(30 - 15) / (30 + 15) = 15 / 45 = 1/3

Now simplify:
3(y - 5) / 3(y + 5)
= (y - 5) / (y + 5)
Substitute y=10:
(10 - 5) / (10 + 5) = 5 / 15 = 1/3

Kapish?

#### Subhotosh Khan

##### Super Moderator
Staff member
I stand corrected.

Stapel's method described above - using a graphing calculator - will tell you DEFINITELY whether you have reduced CORRECTLY or not.

However, it CANNOT tell you whether further simplification is possible or not.

#### scoresofsteel

##### New member
Putting Y = 0 will be a fast way of knowing that.

(3Y - 15) / (3Y + 15)

Put Y = 0

(3*0 - 15) / (3*0 + 15)

-15 / 15

= -1

-----

now put Y = 0 for (Y - 5)/(Y + 5)

(0 - 5)/ (0 + 5)

-5 / 5

= -1 ... matches -1 above

#### stapel

##### Super Moderator
Staff member
ebrushman said:
After I simplify [3y-15 / 3y+15], is there a check to know I'm right?
scoresofsteel said:
Putting Y = 0 will be a fast way of knowing that.
Actually, this technique gets students into a lot of trouble later on, specifically in checking trig identities.

By checking only one point, you only verify that the two expressions evaluate the same at that one point. This is quite a different thing from showing that they are equivalent. :shock:

Eliz.

#### scoresofsteel

##### New member
Yeah thats right, this is something that is known as "necessary but not sufficient condition". If value dont match then they are NOT equivalent, however if the values match...it mean it *might* be correct.