We know that
Multiply both sides by (x − 1).
x2 − 3x + A = (x + B)(x − 1)
Multiply out on the right side.
x2 − 3x + A = x2 + Bx − x − B
Subtract x2 from both sides.
−3x + A = Bx − x − B
Subtract x from both sides of the equation.
−2x + A = Bx − B
Set the x-terms = to each other.
Set the constant terms = to each other.
∴ − 2 = B and A = − B
∴ A = 2
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