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Find constants A and  B such that

 x+7x2x2=Ax2+Bx+1
for all x such that x does not equal -1 and x does not equal 2. Give your answer as the ordered pair.

 Aug 17, 2018
 #1
avatar+33660 
+3

A partial fractions problem:

 

.

 Aug 18, 2018
 #2
avatar+118716 
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Your answer is better than mine Alan. it is better explained.

I rarely touch questions that are presented so poorly. Maybe that is why Lightning reposted. 

Or maybe this question was posted by someone else in his class.

 

Ref for others :  https://web2.0calc.com/questions/help_51906

Melody  Aug 18, 2018
 #3
avatar+1246 
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I didn't double post this one. I would have realized the answer was already answered. Plus, I have a work from 9pm to 3am. So it coudn't be me.

Lightning  Aug 18, 2018
 #4
avatar+1246 
+1

Multiplying both sides by $(x - 2)(x + 1) = x^2 - x - 2$, we get x+7=A(x+1)+B(x2)=Ax+Bx+A2B=(A+B)x+(A2B). Comparing the coefficients on both sides, we obtain the system of equations A+B=1,A2B=7. Subtracting the second equation from the first equation, we get $3B = 1 - 7 = -6$, so $B = -2$. Then from the first equation, $A = 1 - B = 3$. Hence, x+7x2x2=3x22x+1, and our answer is (A,B)=(3,2).

 Aug 19, 2018

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