CPM Homework Help : PCT Problem 6-100

We know that $\frac { x ^ { 2 } - 3 x + A } { x - 1 }= x + B$ for some numbers $A$ and $B$ . Find $A$ and $B$ .

Step 1:

Multiply both sides by $\left(x − 1\right)$ .

$x^{2} − 3x + A = \left(x + B\right)\left(x − 1\right)$

Step 2:

Multiply out on the right side.

$x^{2} − 3x + A = x^{2} + Bx − x − B$

Step 3:

Subtract $x^{2}$ from both sides.

$−3x + A = Bx − x − B$

Step 4:

Subtract $x$ from both sides of the equation.

$−2x + A = Bx − B$

Step 5:

Set the $x$ -terms $=$ to each other.
Set the constant terms $=$ to each other.

Answer:

$∴ − 2 = B$ and $A = − B$
$∴ A = 2$

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