CPhill

4x^3−12x^2 /4x^2+7x−2/ 2x^2−6x / 5x^2+11x+2

Invert the second fraction and multiply by the first

4x^3 - 12x^2               5x^2 + 11x + 2

___________     x     _______________                factor as much as possible

4x^2 + 7x - 2                 2x^2 - 6x

4x^2  ( x - 3)                    ( 5x + 1) ( x + 2)

______________   x      _______________       "cancel"  where possible

 (4x - 1) ( x + 2)                 2x ( x - 3)

2x * ( 5x + 1)

_____________

  ( 4x - 1)

Invert    [ 3 + x ] / x    and multiply by the first fration

[ 2 + x ] / [ 8x ]  *   [x] / [ 3 + x ]  =

[ 2 + x ] [ x ]

____________          cancel  the x's

[ 8x ]  [ 3 + x ]

  2 + x

_________

8 ( 3 + x)

  Yep....good job, Jenny  !!!

I think that you are correct, NSS !!!

I let you in on a secret, RP....

In most of the higher math classes I've had....I've rarely  encountered these types of radicals.....these are mostly " textbook" exercises.....once you have to suffer through this.....you probably won't see this stuff, again  !!!!!

[ Something to look  forward to, huh ???  ]

sqrt ( 9 - [ 3 sin θ ]^2 )    =

sqrt  ( 9  -  9sin^2 θ )  =

sqrt [  9 ( 1 - sin^2 θ ) ]  =

sqrt ( 9 * cos^2  θ )  =

sqrt (9)  *  sqrt ( cos^2 θ )  =

3 cos θ

I think it's  "C"

Reasoning :

"Free responses"    might encourage lengthy  answers which are usually more time-consuming  for the respondent than multiple-choice questions....thus....fewer questionnaires might be completed on time

Good job,  RP  !!!!

Both are correct  !!!

Looks like  "B"  is the only disadvantage, NSS

OK...glad to help  .....!!!!

The second one is easier, RP

√ [5 p^3 ]

_________     =    (1/3) √ [   (5 p^3)  /  (2p^3) ]    

3 √ [2 p^3 ]

The p^3's   will "cancel"     and we are left with

(1/3) √ [ 5 / 2 ]  =      

√ 5

_____            (do you see this  ??? )

3 √2

We want to get rid of the radical in the denominator  [ this is called "rationalizing the denominator" ]

We can do this in this manner.....Multiply top/bottom by √2     and note that √2 *√2  = √4   = 2

√5 * √2

__________

3 √2 * √2

√10

_____

3 * 2

√10

_____

  6