### Home > PC3 > Chapter 4 > Lesson 4.3.1 > Problem4-115

4-115.

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

Multiply both sides by $(x−1)$.

$x^2−3x+A=(x+B)(x−1)$

Expand the right side.

$x^2−3x+A=x^2+Bx−x−B$

Subtract $x^2$ 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.