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 : Simplify the given expression and find the value for $x=-1$.
$\frac{10 x^2+5 x+2 x y+y}{5 x+y}$

Option 1: –1

Option 2: 0

Option 3: 1

Option 4: 2

Question : Simplify the given expression $\frac{(x+3)^3+(x-3)^3}{x^2+27}$.

Option 1: $3x$

Option 2: $x$

Option 3: $4x$

Option 4: $2x$

Question : What is the value of $\frac{4x^2+9y^2+12xy}{144}$?

Option 1: $(\frac{x}{3} + \frac{y}{4})^2$

Option 2: $(\frac{x}{3} + y)^2$

Option 3: $(\frac{x}{4} + \frac{y}{6})^2$

Option 4: $(\frac{x}{6} + \frac{y}{4})^2$

Question : If $X$ is 20% less than $Y$, then find the values of$\frac{Y–X}{Y}$ and $\frac{X}{X–Y}$.

Option 1: $\frac{1}{5}$ and $-4$

Option 2: $5$ and $-\frac{1}{4}$

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

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