Question

Simplify the following rational expression to determine if thegiven simplification is correct. If it is correct, select TRUE. If it isnot correct, select FALSE.— 3122 – 6x + 92 – 3TOLI

Answer 1

Given an expression as below:

$\frac{x-3}{x^2-6x+9}$

Using a partial fraction:

$\frac{x-3}{x^2-6x+9}$$\frac{x-3}{x^2-6x+9}=\frac{A}{x-3}+\frac{B}{x-3}$

Where

$x^2-6x+9=(x-3)^2=(x-3)(x-3)$$\begin{gathered} \frac{x-3}{(x-3)(x-3)} \\ \text{divide both side by x-3, cancel the common factor} \\ \frac{x-3}{(x-3)(x-3)}=\frac{1}{x-3} \end{gathered}$

Therefore the above expression = True