Show that the expression `(x^2-3x+4)/(x^2+3x+4)` lies between `1/7` and 7 for real values of x.

Find the interval in which 'm' lies so that the expression (mx^(2)+3x-4)/(-4x^(2)+3x+m) can take all real values,x in R.

Show that the expression (px^(2)+3x-4)/(p+3x-4x^(2)) will be capable of all values when x is real,provided that p has any value between 1 and 7.

If x is real, then the value of the expression (x^2+14x+9)/(x^2+2x+3) lies between (a) 5 and 4 (b) 5 and -4 (c) -5 and 4 (d) none of these

If x is real, prove that the value of the expression ((x-1)(x+3))/((x-2)(x+4) cannot be between 4/9 and 1.

The expression (x^(2)+2x+1)/(x^(2)+2x+7) lies in the interval; (x in R)