Question

algebra: concepts and connections - plc investigating rational and irrational numbers which rational expression is undefined when ( a = 1 )? (\frac{9a - 3}{3a^2}) (\frac{10a + 6}{-a^2 + 1}) (\frac{6a^2 - 6}{7a + 7}) (\frac{8a^2}{5a - 10})

Explanation:

Step1: Identify undefined condition

A rational expression is undefined when its denominator equals 0. We substitute $a=1$ into each denominator and check if the result is 0.

Step2: Check first expression denominator

Denominator: $3a^2$. Substitute $a=1$:
$3(1)^2 = 3(1) = 3
eq 0$

Step3: Check second expression denominator

Denominator: $5a-10$. Substitute $a=1$:
$5(1)-10 = 5-10 = -5
eq 0$

Step4: Check third expression denominator

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

Step5: Verify fourth expression denominator (optional)

Denominator: $7a+7$. Substitute $a=1$:
$7(1)+7 = 7+7 = 14
eq 0$

Answer:

$\frac{10a+6}{-a^2+1}$