Question

algebra 2 362403-6 fy - 1
benchmark test 2
solve $2x + \frac{12}{x - 3} = \frac{4x}{x - 3}$
a. 2
b. 2, 3
c. 2, -3
d. $\frac{1}{2}$

Explanation:

Step1: Eliminate denominator

Multiply all terms by $x-3$ (where $x
eq 3$):
$$2x(x-3) + 12 = 4x$$

Step2: Expand and simplify

Expand left side, rearrange to standard form:
$$2x^2 - 6x + 12 = 4x$$
$$2x^2 - 10x + 12 = 0$$
Divide by 2:
$$x^2 - 5x + 6 = 0$$

Step3: Factor quadratic equation

Factor the trinomial:
$$(x-2)(x-3) = 0$$

Step4: Check for extraneous solution

Solutions from factoring: $x=2, x=3$. But $x=3$ makes original denominator 0, so it is invalid. Only $x=2$ is valid.

Answer:

A. 2