Question

locate the points of discontinuity for the function f(x)=5x+2/x^2-3x-4

Answer 1

(5x+2)/x²-3x-4
(5x+2)/x²-4x+x-4
(5x+2)/x(x-4)+1(x-4)
(5x+2)/(x+1)(x-4)
x≠-1,4 
so  function f(x) is discontinous at two points -1and 4  because x never equal to -1 and 4

Answer 2

f(x) is discontinuous when the denominator of the function is 0 and hence f(x) tends towards infinity or negative infinity.

x² - 3x - 4 = 
   -4 * 1  =>     sum is -4 + 1 = -3  which is the coefficient of x.
   Hence   ( x -4) ( x + 1) 
  So  f(x) is discontinuous when  x - 4 = 0  or   x + 1 = 0 
             x = 4  or  -1...