help :)

[Danielle058]

Does anyone know how to simplify this? I've been working on it for awhile and can't figure it out....


(√x-2+ 5/√x-2)
X-2

Thanks!

 

[soroban]

Hello, Danielle058!

Does anyone know how to simplify this?

(√x-2+ 5/√x-2)
x-2

. . . . . . . . . . . ____ . . . .5
. . . . . . . . . . √x - 2 + --<u>-----</u>-
. . . . . . . . . . . . . . . . .√x - 2
We have: . ---------------------
. . . . . . . . . . . . . x - 2

. . . . . . . . . . . . . . . . . . . . . . .____
Multiply top and bottom by √x - 2 :

. . . .x - 2 + 5 . . . . . . x + 3
. . . ------------ . = . ------------
. . . (x - 2)^3/2 . . . . .(x - 2)^3/2

 

[Denis]

QUESTION: why do I not see this procedure more often? :

Let a = x-2

[sqrt(a) + 5 / sqrt(a)] / a
= [(a + 5) / sqrt(a)] / a
= (a + 5) / a^(3/2)

 

[stapel]

QUESTION: why do I not see this procedure more often? Let a = ...

Why? Because the students have a hard enough time just doing the algebraic manipulations. Presenting them with an unecessary (even if potentially helpful) substitution is very frequently like presenting a calf with a new gate. :wink:

Eliz.

 

[Denis]

QUESTION: why do I not see this procedure more often? Let a = ...

Why? Because the students have a hard enough time just doing the algebraic manipulations. Presenting them with an unecessary (even if potentially helpful) substitution is very frequently like presenting a calf with a new gate. :wink: Eliz.

Agree...my point is it's easier to "manipulate / type / write"
x than a-?+?...; like easier to bounce one basketball than 2