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Question 1.

There are numbers a and b for which

\(\frac A{x-1}+\frac B{x+1}=\frac{x+2}{x^2-1}\)

for every number \(x\neq\pm1\). Find b.

 

Question 2.

If h>0, find all values of h such that \(\lceil h\rceil\cdot\lfloor h\rfloor=72\). Express your answer using interval notation.

 Nov 28, 2020
 #1
avatar+115955 
+1

(1)    Note  x^2 - 1  = (x - 1) (x + 1)

 

        x + 2                        A                 B

____________   =    _______  +   _____                      multiply through by (x - 1) ( x + 1)       

(x - 1) ( x + 1)               x - 1            x + 1

 

 

x + 2 =   A ( x + 1)  +  B ( x - 1)      simplify  as

 

1x + 2 =  (A + B)x  + (A - B)

 

Equating terms we have that

 

A + B  =  1

A - B  = 2      add these equations

 

2A  = 3

A = 3/2

 

And

 

3/2 + B = 1

B = -1/2

 

CORRECTED ANSWER   !!! 

 

cool cool cool

 Nov 28, 2020
edited by CPhill  Nov 28, 2020
 #2
avatar+312 
+1

Thanks so much for all the help. I read your solution and I think you did everything great exept you kinda got a and b mixed up.

 Nov 28, 2020
 #4
avatar+115955 
0

Oops....let me fix that  !!!

 

cool cool cool

CPhill  Nov 28, 2020
edited by CPhill  Nov 28, 2020
edited by CPhill  Nov 28, 2020
 #3
avatar+115955 
+1

2)  Note  that

 

9  * 8  =  72

 

So  ceiling  8....  = 9

And floor  8.....  =   8

 

This indicates  that  the solution is

 

(  8 < h < 9 )

 

 

cool cool cool

 Nov 28, 2020

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