What is this radical expression simplified?

Factor the numerator and denominator:

(3k^2 - 84k + 588) / (784 - 4k^2)

= 3(k² - 28k + 196) / [4(196 - k²)]

= (3/4)(k - 14)² / [(14 - k)(14 + k)]

Note that if k = 14, the unfactored expression evaluates to 0/0 which is indeterminate. On the other hand, if k = -14, the expression evaluates to 2352/0 which is undefined.

Ans: The only value of k which makes the expression undefined is k = -14.

k = 14 makes the expression indeterminate which is not the same as undefined.

3k² - 84k + 588      3 (k² - 28k + 196)

-------------------- = --------------------------

    784 - 4k²               28² - (2k)²

                            3 (k-14)(k-14)

                        = -------------------

                            4(14+k)(14-k)

3k² - 84k + 588

-------------------- is undefined when k = ± 14 ...............ANS

    784 - 4k²              

No values "make k undefined."  However, if k = +/-14, the whole expression is undefined, as its denominator is then zero.

To simplify the given expression, let's try to factor the top and bottom:

[3*(k^2 - 28k + 196)] / [4*(196 - k^2)]

= [3*(k - 14)^2] / [4*(14-k)(14+k)]

= 3(14 - k)/[4*(14+k)].

(3k^2 - 84k + 588) / (784 - 4k^2)

= 3(k^2 - 28k + 196) / 4(196 - k^2)

= -(3 (k - 14))/(4 (k + 14)) (for k!=14)