CPM Homework Help : PC3 Problem 4-115

$\frac{x^2-3x+A}{x-1}=x+B$ for some numbers $A$ and $B$ . Determine the values of $A$ and $B$ .

Step 1:

Multiply both sides by $(x−1)$ .

$x^2−3x+A=(x+B)(x−1)$

Step 2:

Expand 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.