Question : Find the value of the expression $\frac{x^2-1}{x-1}-\frac{x^2-9}{x-3}$.

Option 1: 1

Option 2: –2

Option 3: –1

Option 4: 2

Question : Simplify the given expression. $\frac{x^3+y^3+z^3-3 x y z}{(x-y)^2+(y-z)^2+(z-x)^2}$

Option 1: $\frac{1}{3}(x+y+z)$

Option 2: $(x+y+z)$

Option 3: $\frac{1}{4}(x+y+z)$

Option 4: $\frac{1}{2}(x+y+z)$

Question : The value of $x$ in the expression $\tan^{2}\frac{\pi }{4}-\cos^{2}\frac{\pi }{3}=x\sin\frac{\pi }{4}\cos\frac{\pi }{4}\tan\frac{\pi }{3}$ is:

Option 1: $\frac{2}{\sqrt{3}}$

Option 2: $\frac{3\sqrt{3}}{4}$

Option 3: $\frac{1}{\sqrt{3}}$

Option 4: $\frac{\sqrt{3}}{2}$

Question : If $x+\frac{1}{x}=3$, then the value of $\frac{3x^{2}-4x+3}{x^{2}-x+1}$ is:

Option 1: $\frac{4}{3}$

Option 2: $\frac{3}{2}$

Option 3: $\frac{5}{2}$

Option 4: $\frac{5}{3}$

Question : The 12th term of the series $\frac{1}{x}+\frac{x+1}{x}+\frac{2x+1}{x}+...$ is:

Option 1: $\frac{11x+1}{x}$

Option 2: $\frac{12x+1}{x}$

Option 3: $\frac{x+12}{x}$

Option 4: $\frac{x+11}{x}$