IF x is real and `0ltmlt1`, show that the expression `(x^2+2x+m)/(x^2+4x+3m)` is capable of assuming all real values.

If x is real , show that each of the following expressions is capable of assuming all real values: (2x^2+4x+1)/(x^2+4x+2)

If x is real , show that each of the following expressions is capable of assuming all real values: p^2/(1-x)-q^2/(1+x)

If x is real , show that each of the following expressions is capable of assuming all real values: (2x^2+5x+2)/(x^2+6x+7)

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 , show that the expressions (x^2-ab)/(2x-a-b) has no real value between a and b.

If x is real show that the expressions (x^2+34x-71)/(x^2+2x-7) has no value between 5 and 9.

If x is real show that the expressions (3x-5)/(x^2-1) has no value between 1/2 and 9/2 .

If x is real show that the expressions ((x-1)(x+3))/((x-2)(x+4)) has no value between 4/9 and 1.

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

For what real values of x the expressions x^2-2x+3 is negative?