Question

Solve for A and B:

13x+1/2x^2+3x-2 = A/2x-1 + B/x+2

I don't know how to proceed with solving something with three unknowns.

Answer 1

Here is the equation in a more readable form (see attached file)

Answer 2

\[(13x + 1)/(2x ^{2} +3x - 2) = (A(x + 2) + B(2x -1) / (2x ^{2} +3x -2)\]
\[13x + 1 = Ax + 2A + 2Bx - B\]
13x = Ax + 2Bx
13 = A + 2B
1 = 2A -B
solve last two equation for A and B

Answer 3

The answer for A = 3 and B = 5. That does not give me 3 or 5.

Answer 4

It does.
B = 2A -1
13 = A + 2(2A - 1)
13 = A + 4A - 2
13+ 2 = 5 A
15 = 5 A
A = 3

Answer 5

there is a fairly snappy way to do this

Answer 6

\[\frac{13x+1}{(2x-1)(x+2)}\] to find B replace \(x\) by \(-2\) and cover up that factor in the denominator
\[B=\frac{13\times -2+1}{2\times -2-1}=\frac{-25}{-5}=5\]

Answer 7

@satellite73 Your way is much better but I haven't read about it so can you please explain.

Answer 8

I followed you, sangya21, to this point:

13x+1 = Ax + 2A + B2x - B

But I don't get how you got rid of 2A and -B from the equation.

Answer 9

I just equated constant at one side and variables at other
13x = Ax + 2Bx ( equating x variables on LHS to RHS)
1 = 2A - B ( equating constants)