+0  
 
-2
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avatar+819 

I need help with algebra

 

Find constants $A$ and $B$ such that
\[\frac{2x + 11 - x - 13}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\]
for all ${}x$ such that $x\neq -1$ and $x\neq 2$.

 Aug 17, 2023
 #1
avatar+128826 
+1

Note that x^2 - x - 2  can  be  factored as   (x - 2) ( x + 1)

Multiply the equation  through by this factorization and we  get

 

2x + 11  - x - 13 =  A(x + 1) + B ( x -2)

 

x - 2  = A(x + 1) +  B ( x -2)

 

1x - 2  = (A + B)x  + A - 2B             equting  coefficients  on  both sides  of the eqution  we have

 

1 = A + B

-2 =A - 2B

 

Multiply the second equation  through by -1

 

1 = A + B

2 = -A + 2B          add these

 

3 = 3B

So B = 1

 

And

A + B = 1

So A  =   0

 

cool cool cool

 Aug 17, 2023

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