Question

(20 points)

Answer 1

The excluded values are the values that the variable cannot take on because it makes the overall expression undefined.

For example, we can't have $x=0$ in the expression $\dfrac1x$ because $\dfrac10$ is undefined.

For both of these problems you do the same sort of thing, with some factorization along the way:

$\dfrac{9p^2}{4p^2-12p}=\dfrac{9p^2}{4p(p-3)}$

If $p=0$ or $p=3$, the denominator is 0 and we have an undefined expression, so these are the excluded values.

$\dfrac6{m^2+m-42}=\dfrac6{(m+7)(m-6)}$

If $m=-7$ or $m=6$, we get an undefined expression.