Question

question #10
simplify the rational expression $\frac{4x^{2}-8x + 3}{4x^{2}-12x + 9}$
$\frac{2x + 1}{2x - 3}$
$\frac{2x - 1}{2x - 3}$
$\frac{2x + 1}{2x + 3}$
$\frac{2x - 1}{2x + 3}$

Explanation:

Step1: Factor the numerator

For $4x^{2}-8x + 3$, we need two numbers that multiply to $4\times3 = 12$ and add up to $-8$. The numbers are $-2$ and $-6$. So, $4x^{2}-8x + 3=4x^{2}-2x-6x + 3=2x(2x - 1)-3(2x - 1)=(2x - 1)(2x - 3)$.

Step2: Factor the denominator

For $4x^{2}-12x + 9$, it is in the form of $a^{2}-2ab + b^{2}=(a - b)^{2}$, where $a = 2x$ and $b = 3$. So, $4x^{2}-12x + 9=(2x - 3)^{2}$.

Step3: Simplify the rational - expression

$\frac{4x^{2}-8x + 3}{4x^{2}-12x + 9}=\frac{(2x - 1)(2x - 3)}{(2x - 3)^{2}}=\frac{2x - 1}{2x - 3}$ (assuming $x
eq\frac{3}{2}$).

Answer:

B. $\frac{2x - 1}{2x - 3}$