Question

algebra: concepts and connections - plc
adding and subtracting rational expressions
which values of x will make the expression \\(\frac{6x^2 - 54}{5x^2 - 20}\\) equal to 0? choose two correct answers.
options: -2, 2, -3, 0, 3

Explanation:

Step1: Set numerator equal to 0

A rational expression equals 0 when its numerator is 0 (and denominator is not 0).
$$6x^2 - 54 = 0$$

Step2: Isolate the $x^2$ term

Add 54 to both sides, then divide by 6.
$$6x^2 = 54$$
$$x^2 = \frac{54}{6} = 9$$

Step3: Solve for $x$

Take square root of both sides.
$$x = \pm\sqrt{9} = \pm 3$$

Step4: Verify denominator is non-zero

Check $x=3$: $5(3)^2 - 20 = 45 - 20 = 25
eq 0$
Check $x=-3$: $5(-3)^2 - 20 = 45 - 20 = 25
eq 0$
Both values are valid.

Answer:

-3, 3