Question

What is the quotient of c^2-c-2/c^2-1 divided by c^2+3c +2/c^2-3c+2 in lowest terms?

A. (C-2)/(c-1)
B. (C+1)(c+2)/(c-1)^2
C. (C-2)^2/(c+1)(c+2)
D. (C-2)/(c+1)

Answer 1

hello

Answer 2

Hi @Zenmo

Answer 3

Apply the reciprocal identity for division \[\frac{ \frac{ a }{ b } }{\frac{ c }{ d } } = \frac{ a }{ b } \times \frac{ d }{ c }\] to your equation.

Answer 4

So
C^2-c-2/c^2-1 x c^2-3c+2/c2+3c+2
@Zenmo

Answer 5

Yes. Now, we look for "stuffs" that can be factored. Do you know how to factor an equation like \[x^2+7x+10\]?

Answer 6

I can if you give me list of options. If there isn't then no... Not that I remember of. @Zenmo

Answer 7

\[x^2+7x+10\]

Let us start with 10: what two numbers multiply into 10?

Answer 8

List all the combinations

Answer 9

5 x 2
1 x 10
@Zenmo

Answer 10

Next, look at the following set of numbers that multiply to 10, which set adds to 7?

Answer 11

5 & 7. @Zenmo

Answer 12

5 x 7 = 35
5 + 7 = 12
These do not meet the requirement of two numbers adding to 7 while also multiplying to 10.

Answer 13

So oops I meant 5 +2 sorry @zenmo

Answer 14

Why 5 and 2?

Answer 15

It adds up to 7 and multiples to 10. So the factoring would be (x+5)(x+2) right? @zenmo

Answer 16

Yes, and you understood on how you factored it?

Answer 17

Yes. @zenmo

Answer 18

Now, let us go back to your equation, \[c^2-c-2\]. Look at the 2nd term of " -c " and the 3rd term " 2 "

Answer 19

what is the number of the 2nd term?

Answer 20

-1 @zenmo

Answer 21

Yes, what is the number of the third term?

Answer 22

Let me know if you are stuck.

Answer 23

-2. @zenmo.
Soo (x+1)(x-2) right?

Answer 24

For the factoring.. & I just noticed you didn't even ask for the factors.. Sorry. @zenmo

Answer 25

Yes

Answer 26

\[\frac{ (x+1)(x-2) }{ c^2-1 } \times \frac{ c^2-3c+2 }{ c^2+3c+2 }\]

Answer 27

Good so far?

Answer 28

Yes. @zenmo

Answer 29

Now, we look for other parts that can be factored. Let us finished the left side of the multiplication. What is the factor of \[c^2-1\]?

Answer 30

Hint: \[a^2-b^2 = (a+b)(a-b)\] Identity

Answer 31

(C+1)(c-1) @zenmo

Answer 32

Yes, correct. Now, the right side also looks to be factorable. Let us start with the numerator. Can you factor c2-3c+2

Answer 33

Yeah. (X-2)(X-1) right? @zenmo

Answer 34

Yes, correct, now, there is only one remaining. Factor c2+3c+2

Answer 35

(X+1)(X+2) @zenmo

Answer 36

\[\frac{ (c+1)(c-2) }{ (c+1)(c-1) }\times \frac{ (c-2)(c-1) }{ (c+2)(c+1) }\] it is not factored based on the work we just did.

Answer 37

Do you know how to cancel?

Answer 38

it is now factored*

Answer 39

I think I know how to cancel, but I probably don't.... @zenmo