Question

Help with restrictions?

Answer 1

What is the restriction on the product of \[\frac{ x^2+3x+2 }{ x^2-2x-3 } * \frac{ x^2+4x+3 }{ x+2 }\]

Answer 2

@wio

Answer 3

@satellite73

Answer 4

Shhh, I got disconnected...

x can't be equal if that makes your expression/function undefined.
It will be undefined when \(\large\color{black}{ \rm denominator=0 }\).

Answer 5

Set: \(\large\color{black}{ x^2-2x-3=0 }\)
and \(\large\color{black}{ x+2=0 }\)

and find \(\large\color{black}{ \rm ALL }\) the values of x (where any of the denominators will be zero)

Answer 6

I don't understand..

Answer 7

Do you know how to factor?

Answer 8

I believe so!

Answer 9

Can you factor all of the quadratic expressions?

Answer 10

When I factored the equation I got\[\frac{ (x+2)^2 }{ (x-3)(x+1)(x+3) }\]

Answer 11

That doesn't make any sesne

Answer 12

Wow that was a sentence. But yes, that's the equation I got when I factored.

Answer 13

Wait...

Answer 14

first of all, you find the restictions BEFORE you find the product.

Answer 15

The denominator can only have 3 binomial factors, and \(x+2\) is one of them.

Answer 16

solve the equations I set for you, please. Can you at least solve the second one, the x+2=0 ?

Answer 17

Is that any closer?

Answer 18

\[
x^2-2x-3 = x^2-3x+x-3 = x(x-2)+1(x-3) = (x+1)(x-3)
\]

Answer 19

When you multiply you get: \[
\frac{\ldots}{(x+1)(x-3)(x+2)}
\]This means the denominator is zero when \(x=-1\), \(x=3\), or \(x=-2\).

Answer 20

Oh dear. Now I'm REALLY confused.

Answer 21

I just factored and multiplies the denominators. You said you know how to factor.

Answer 22

@SolomonZelman : The first equation equals (x-3)(x+1). The second equation equals -2.
@wio : I do. But how do I know which are the restrictions? Do I plug them in?

Answer 23

The restrictions are division by zero

Answer 24

So for example \(x\neq -1\) is a restriction.

Answer 25

Okay. They gave me the choices of \[x \neq-2 , x \neq1, x \neq3, x \neq-3\]

Answer 26

Okay, plug the restrictions into the numerators. If the numerator is 0 as well, then I suppose they are allowing us to factor it out and exclude it.

Answer 27

Okay, I plugged in -3 and got zero.

Answer 28

You want to try -1, 3, and -2

Answer 29

-1 gave me zero as well, 3 did not give me zero, and -2 gave me 0.

Answer 30

So is 3 my answer?

Answer 31

Yes

Answer 32

Ohhh! Okay. I got it now. Thank you so much for your patience!

Answer 33

Okay, so you learned it.

Answer 34

Yes, I understand the concept, now. :)