Question

algebra: concepts and connections - plc
adding and subtracting rational expressions
which rational expression is undefined when ( x = 0 )?
( \frac{5x^2 - 4}{3x - 3} )
( \frac{6x^2}{9x - 3} )
( \frac{8x + 6}{-x^2 + 1} )
( \frac{4x - 8}{-2x^2} )

Explanation:

Step1: Recall undefined condition

A rational expression is undefined when its denominator equals 0. We substitute $x=0$ into each denominator and check if the result is 0.

Step2: Check first expression denominator

Denominator: $3x-3$. Substitute $x=0$:
$3(0)-3 = -3
eq 0$

Step3: Check second expression denominator

Denominator: $9x-3$. Substitute $x=0$:
$9(0)-3 = -3
eq 0$

Step4: Check third expression denominator

Denominator: $-x^2+1$. Substitute $x=0$:
$-(0)^2+1 = 1
eq 0$

Step5: Check fourth expression denominator

Denominator: $-2x^2$. Substitute $x=0$:
$-2(0)^2 = 0$

Answer:

$\boldsymbol{\frac{4x-8}{-2x^2}}$