If P = $\frac{x+1}{x-1}\backslash frac\{x+1\}\{x-1\}$ and Q =  $\frac{x-1}{x+1}\backslash frac\{x-1\}\{x+1\}$ then $P^2+Q^2-2PQP^2+Q^2-2PQ$ = ……………

The rational expression A = $(\frac{x+1}{x-1}-\frac{x-1}{x+1}-\frac{4x}{x^2+1})\backslash left(\backslash frac\{x+1\}\{x-1\}-\backslash frac\{x-1\}\{x+1\}-\backslash frac\{4x\}\{x^2+1\}\backslash right)$ is multiplied with the additive inverse of B = $\frac{1-x^4}{4x}\backslash frac\{1-x^4\}\{4x\}$ to get C, then C = ……………

The product of $\frac{x^2-4}{3-x}\backslash frac\{x^2-4\}\{3-x\}$ and additive inverse of $\frac{x^2-9}{2+x}\mathrm{.}\backslash frac\{x^2-9\}\{2+x\}.$

If (x – 1) and (x + 3) are the factors of $x^3+3x^2\text{–}x\text{–}3x^3\; +\; 3x^2\; –\; x\; –\; 3$ then the other factor is ……

A rational expression whose numerator is a quadratic polynomial with zeroes, 1 and 2 and whose denominator is monomial with zero 3 is ………………

Simplify $\frac{(a^2-b^2{)}^3+(b^2-c^2{)}^3+(c^2-a^2{)}^3}{(a-b{)}^3+(b-c{)}^3+(c-a{)}^3}\backslash frac\{(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3\}\{(a-b)^3+(b-c)^3+(c-a)^3\}$

Find "a" and “b” in order that $x^3\text{–}6x^2+ax+bx^3\; –\; 6x^2\; +\; ax\; +\; b$ may be exactly divisible by $x^2\text{–}3x+2.x^2\; –\; 3x\; +\; 2.$

If g(x) $=x^6+3x^4\text{–}24x^2+3=\; x^6\; +\; 3x^4\; –\; 24x^2\; +\; 3$ find g(1), g(2) and g(3).

If the zeroes of the rational expression (3x + 2a) (2x + 1) are $\frac{-1}{2}\backslash frac\{-1\}\{2\}$ and $\frac{b}{3}\backslash frac\{b\}\{3\}$ then the value of a is ………………

If ‘a’ and ‘b’ are unequal and $x^2+ax+bx^2\; +\; ax\; +\; b$ and $x^2+bx+ax^2\; +bx\; +\; a$ have a common factor, then a + b = ……………