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

For real values of x, the value of expression (11x^2-12x-6)/(x^2+4x+2)

If x is real, show that the expression (4x^2+36 x+9)/(12 x^2+8x+1) can have any real value .

If x is real, the maximum and minimum values of expression (x^(2)+14x+9)/(x^(2)+2x+3) will be

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 is real, prove that the quadratic expression (i) (x-2)(x+3)+7 is always positive. (ii) 4x-3x^(2)-2 is always negative.

Given that for all real x, the expression (x^(2)-2x+4)/(x^(2)+2x+4) lies between (1)/(3) and 3 the values between which the expression (9tan^(2)x+6tanx+4)/(9tan^(2)x-6tanx+4) lies are