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

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

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 (9.3^(2x)+6.3^x+4)/(9.3^(2x)-6.3^x+4) lies are

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

Find the values of a for which the expression (ax^2+3x-4)/(3x-4x^2+a) assumes all real values for all real values of x

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

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

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

If x is real, the expression (x+2)/(2x^2 + 3x+6) takes all value in the interval