Question

$\frac{4x}{x - 2}-\frac{3}{x - 1}
\frac{ax^{2}+bx + c}{(x - 2)(x - 1)}
a=

b=

c=$

Explanation:

Step1: Find a common - denominator

First, find a common denominator for $\frac{4x}{x - 2}-\frac{3}{x - 1}$. The common denominator is $(x - 2)(x - 1)$. So, $\frac{4x}{x - 2}-\frac{3}{x - 1}=\frac{4x(x - 1)-3(x - 2)}{(x - 2)(x - 1)}$.

Step2: Expand the numerator

Expand $4x(x - 1)-3(x - 2)$:
\[

$$\begin{align*} 4x(x - 1)-3(x - 2)&=4x^{2}-4x-3x + 6\\ &=4x^{2}-7x + 6 \end{align*}$$

\]
Since $\frac{4x^{2}-7x + 6}{(x - 2)(x - 1)}=\frac{Ax^{2}+Bx + C}{(x - 2)(x - 1)}$, then $A = 4$, $B=-7$, $C = 6$.

Answer:

$A = 4$
$B=-7$
$C = 6$