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avatar+68 

Fill in the blanks to make a true equation:

1/n(n+3)=blank/n+blank/n+3.

 Apr 7, 2024
 #1
avatar+214 
+1

Are the 2 blanks equal or not?

 #2
avatar+68 
+1

They are not equal

SilviaJendeukie  Apr 7, 2024
 #3
avatar+128794 
+1

\(1/n(n+3)=blank/n+blank/n+3. \)

 

1/ [n (n + 3)] = A / n  + B /(n + 3)

 

Multiply through by  n (n + 3)

 

1 =  A ( n + 3)  + B(n)

 

1 = (A + B)n  + 3A

 

Equate terms

 

A + B  = 0

3A   =1  →  A =1/3

 

So B = -1/3

 

Check     

 

(1/3) / n   - (1/3) / ( n + 3)  =

 

[(1/3)(n + 3)  - (1/3) n] / (n (n + 3))

 

[ (1/3 n  + 1  - 1/3 n ]  / [n ( n + 3)]  = 

 

1 / [ n ( n + 3) ]

 

So

 

first blank = 1/3

second blank  =  -1/3

 

 

cool cool cool

 Apr 7, 2024
edited by CPhill  Apr 7, 2024
 #4
avatar+214 
+1

Thanks CPhill for covering up for mesmiley


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