Question

need help!!! urgent will award medal!!!

Answer 1

what is the restriction point of this

Answer 2

What is the restriction on the product of

Answer 3

@quickstudent @Whitemonsterbunny17 @worldsgreatest @Elsa216 @Cosmichaotic @study100

Answer 4

A fraction means a division.
Have you heard of a division which is undefined?

Answer 5

the restriction point? so only 1.
I guess you have to factor our those trinomials.

Answer 6

Specifically, dividing by what is undefined?

Answer 7

well, with just looking at the equation now? @mathstudent55

Answer 8

it wants the restriction on the product

Answer 9

@rayanashef98
Let me ask again.
You can take any number and divide by anything you want, except by one single number.
What is the number you can't divide by because division by that number is undefined?

Answer 10

these are the options:
, x ≠ -3
x ≠ 3
x ≠ 1
x ≠ -2

Answer 11

would it be 0 @mathstudent55

Answer 12

Exactly.

Answer 13

Division by 0 is not allowed.

Answer 14

@mathstudent55 seriously math, you need to become a math teacher :))

Answer 15

then you'll be mathteacher55 :))

Answer 16

Remember, a fraction is a division of a numerator by a denominator.
In your expression, you have 2 fractions.
Each fraction has a denominator.
Each denominator is an expression is x.
Any value that causes either denominator to be zero must be excluded because, as you well know, division by zero is not allowed.

Answer 17

Now we begin by ignoring the numerators and only thinking about the denominators.

Answer 18

ok

Answer 19

Let's look at the right denominator only because it's a simpler expression and we'll deal with it faster.

Answer 20

alright

Answer 21

The right denominator is x + 2.
The expression x + 2 may or may not equal zero, depending on what x is equal to.
We need to find out what value of x would make the expression x + 2 equal zero.
We do the opposite of what we want.
We purposely set x + 2 equal to zeros and solve for x.

Answer 22

x=2

Answer 23

x + 2 = 0

Subtract 2 from both sides to get:

x + 2 - 2 = 0 - 2

x = -2

Answer 24

right -2

Answer 25

We found one restriction: \(x \ne -2\)
x cannot be -2.

Answer 26

ok

Answer 27

so that is the answer then

Answer 28

bc its multiple choice so it only can be one of them

Answer 29

Now we need to do the same to the left denominator.
Again we do the opposite of what we want.
We don't want the denominator to equal zero, so we set it equal to zero to find the values of x that cause a zero in the denominator.
Then those values will be restrictions on x.

Answer 30

Not so fast. Let's continue.

Answer 31

ok

Answer 32

Now we set the left denominator also equal to zero and we solve for x.

\(x^2 - 2x - 3 = 0\)

We factor the left side:

\((x - 3)(x + 1) = 0\)

We set each factor equal to zero:

\(x - 3 = 0\) or \(x + 1 = 0\)

We solve each small equation:

\(x = 3\) or \(x = -1\)

Answer 33

ok

Answer 34

so x can't equal 3 -1 or 2

Answer 35

Correct.

Answer 36

thnx

Answer 37

technically math is right! :)
but after the product, one answer remains
x cannot be equal to 3

Answer 38

Now we do one more step.
We actually multiply the fractions together, factor the numerators, and reduce as much as possible.

Answer 39

\(\dfrac{x^2 + 3x + 2}{x^2 - 2x - 3} \times \dfrac{x^2 + 4x + 3}{x + 2} \)

\(= \dfrac{(x + 2)(x + 1)(x + 3)(x + 1)}{(x - 3)(x + 1) (x + 2)} \)

Now we simplify the fractions (we reduce it):

\(= \dfrac{\cancel{(x + 2)}\cancel{(x + 1)}(x + 3)(x + 1)}{(x - 3)\cancel{(x + 1)}\cancel{(x + 2)}} \)

\(= \dfrac{(x + 3)(x + 1)}{x - 3}\)

From here you see that the only denominator that remains is x + 3, so only x = -3 is a restriction.

Answer 40

oh @mathstudent55 x=3

Answer 41

denominator is x-3

Answer 42

Thanks for the correction.
It's great to see that at least you are still awake! That makes one of us awake.
Thanks.
Since the denominator has x - 3, we set x - 3 = 0 and we get x = 0 as the restriction.

Answer 43

Everything is explained so well.
I actually crossed our wrong factors when I did the problem haha. :P
Good work!

Answer 44

Sleep if you're tired! Your health is uttermost important. :)

Answer 45

Oh I was horrible when I'm tired too haha xD I did the problem all wrong once when I was half asleep. Hope to see you again soon mathstudent!

Answer 46

It's only 8:05 pm here, but my half dead state starts kicking in around 10 PM

Answer 47

Actually I think there is a problem with this problem.
Once you simplify the expression to

\(\dfrac{(x + 3)(x + 1)}{x - 3}\)

then the restriction of x = 3 is still apparent because it is still visible in the denominator.
Since the binomials x + 1 and x + 2 are no longer in the denominator, those restrictions must be mentioned.

Therefore,

\(\dfrac{x^2 + 3x + 2}{x^2 - 2x - 3} \times \dfrac{x^2 + 4x + 3}{x + 2}\) = \(\dfrac{(x + 3)(x + 1)}{x - 3}\) for \(x \ne -2\) and \(x \ne -1\)

Answer 48

You still have 2 hours then.
I need to go.
Bye.

Answer 49

Bye! See you again soon! :)
Have a good rest ! <3

Answer 50

Thanks. Good night.

Answer 51

i need help with another!! @study100

Answer 52

What is the restriction on the product of

Answer 53

@study100 r u there?

Answer 54

I'm here :)
Sorry I had to take care of my baby cousin

Answer 55

https://drive.google.com/file/d/0BxHGvu5cxsDlbVdqS2hNeFhmOHlBbjQydVBFdk91NlZUemNJ/edit?usp=sharing

Answer 56

thnx @study100

Answer 57

You're welcomed :)