If x is real show sthat the value of `(x^(2)+2x+3)/(x^(2)+2x+4)` always lies between `2/3` and 1.

If x be real, prove that the value of (11x^(2)+12x+6)/(x^(2)+4x+2) cannot lie between -5 and 3.

If x be real, prove that the value of (2x^(2)-2x+4)/(x^(2)-4x+3) cannot lie between -7 and 1.

If x is real , then the minimum value of (x^(2)-3x+4)/(x^(2)+3x+4) is :

If x is real , then the maximum value of (x^(2)+14x+9)/(x^(2)+2x+3) is

If x is real, then the value of the expression (x^2+14 x+9)/(x^2+2x+3) lies between

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.

If x be real, find the maximum value of ((x+2))/(2x^(2)+3x+6) .

Find the maximum value of (7−x)^4 (2+x)^5 when x lies between −2 and 7 .

Find the ranges of the values of x for which x^(2)-4x+2 lies between -1 and +1.