need help with math: listing all the values for which the expression is undefined?

Question

1) 6x-7 2) p^2 - 11p
_________ ___________
x^2 - 13x - 48 p^2 - 9p - 22

_________ = divide

please show some work

Answer 1

The expression is undefined when the denominator is zero. The result is a simple quadratic equation:

Problem 1: Undefined when:

x^2 - 13x - 48 = 0
(x - 16)(x + 3) = 0

x = 16 or x = -3. (Those are the two values where the expression is undefined.)

Problem 2:

p^2 - 9p - 22 = 0
(p - 11)(p + 2) = 0

p = 11 or p = -2

Note, though that the numerator of problem 2 (p^2 - 11p) is equal to p(p-11). As a result, (p-11) factors out of both the numerator and demoninator of the second expression, so it reduces to p/(p+2), which is only undefined where p=-2.

As written, it is undefined (0/0) where p=11 as well, but if simplified, the simplified form is undefined only where p=-2.

As an alternative, the quadratic equation could be used to solve these, if you can't see the factoring by looking at them:

x^2 - 13x - 48 = 0
x = (13 +/- sqrt(13^2 - 4*1*(-48)))/2
x = (13 +/- sqrt(361))/2
x = (13 +/- 19)/2
x = -6/2, x = 32/2
x = -3, x = 16

p^2 - 9p - 22 = 0
p = (9 +/- sqrt(9^2 - 4*1*-22)))/2
p = (9 +/- sqrt(169))/2
p = (9 +/- 13)/2
p = -4/2, p = 22/2
p = -2, p = 11