Question

What is the product in simplest form? State any restrictions on the variable.

2x-8/x^2-16 • x^2+5x+4/x^2+8x+16

Answer 1

Wow... this is gonna be a mess... how are your factoring skills ??

Answer 2

Just to check ... is the problem the same as
\[ \frac{2x-8}{x^2-16} \cdot \frac{x^2+5x+4}{x^2+8x+16}\]

Answer 3

@cruffo yea that's the problem

Answer 4

ok. I would suggest factoring all numerators and denominators first, in case we can simplify, and to check for those "restrictions" the question asked about.

Answer 5

Can u explain or show me how to factor the numerators and denominators? Idk how to do that part.

Answer 6

\[\frac{ 2(x-4) }{ (x-4)(x+4) } \times \frac{ (x+4)(x+1) }{ (x+4)(x+4) }\]

Answer 7

use formula difference of two squares

Answer 8

Can you simplify it?

Answer 9

What Aveline's answer is showing is the factored form. She had to use a number of techniques to do that. Do any of those factorization **not ** make sense?

Answer 10

That makes sense, what do I do after its in factored form?

Answer 11

what mean restrictions in this case ? how you think ?

Answer 12

Would the answer be 2=x+1?

Answer 13

The "restrictions" that they are talking about are numbers that make the denominator in either fraction 0. Remember : #/0 is undefined.

Answer 14

No, the goal is not to "solve", but to multiply.

Answer 15

yes cruffo you are right

Answer 16

Ah okay sorry I'm so confused

Answer 17

the denominator zero make the fractions undefined

Answer 18

For the point of Aveline's answer, what numbers make the denominator 0? Hint, there are two such numbers...

Answer 19

On the left side, cross off the two (x-4)'s on the top and bottom. They equal 1 anyway so they cancel out. On the right side, do the same thing with the two (x+4)'s:
\[\frac{ 2 }{ (x+4) } \times \frac{ (x+1) }{ (x+4) }\]

Answer 20

This is too busy...

Answer 21

Okay so... 2 and 1 would be the restrictions?

Answer 22

@cruffo am I right?

Answer 23

Well the equation simplifies to \[\frac{ (2)(x+1) }{ (x+4)(x+4) }\]
If we plug in -4 for x, the bottom of the equation is equal to 0. Therefore, the restriction is x=-4

Take a look for yourself. X can not equal -4
https://www.desmos.com/calculator/ofx8rjslpa

Answer 24

Okay I got it, thank you guys so much !! Aveline could you please help me with one more problem?

Answer 25

@aveline please help !!
Solve the following equation and check the solution.

4/x-2 = x-1/x-2