SOLUTION: Find A and B: A/x+2 + B/x-1 = 7x+2/x^2+x-2

Question 475968: Find A and B: A/x+2 + B/x-1 = 7x+2/x^2+x-2
Found 2 solutions by tinbar, solver91311:
Answer by tinbar(133) (Show Source): You can put this solution on YOUR website!
A/x+2 + B/x-1 = A(x-1)+B(x+2)/x^2+x-2 = 7x+2/x^2+x-2
simplifying the numerator, we get Ax-A+Bx+2B = (A+B)x + (2B-A) = 7x+2
so we know A+B = 7 and 2B-A = 2
from A+B=7, we have A=7-B, which we can plug into the second equation to get 2B-(7-B)=2 which gives us B=3, and so for A+B=7 to be true, we need A=4
Therefore, A=4, and B=3
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Notice that the denominators in the LHS are the factors of the denominator in the RHS. That is to say that the RHS denominator is the LCD of the two fractions in the LHS. Apply the LCD and add the two fractions:

Distribute and collect:

Multiply both sides by the common denominator:

Clearly:

and

Solve the 2X2 system for A and B

John

My calculator said it, I believe it, that settles it

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