Let's factor the denominator, because the denom. is where restrictions usually originate.
2x^2 - 3x - 35 = (2x + 7)(x - 5). Note that 7x - 10x = -3, which agrees with the middle term of 2x^2 - 3x - 35.
So the given rational fraction has the denominator (2x + 7)(x - 5).
Set each of these factors = to 0, separately, and find the x-value in each case:
x-5=0 => x = 5
2x + 7 = 0 => 2x = -7, so that x = -7/2.
All x are permitted in the denominator OTHER THAN {-7/2, 5}.
