Find the Symmetry f(x)=(x^2+x-2)/(x-6)

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -2}$ and whose sum is ${\displaystyle 1}$.

Write the factored form using these integers.

Find ${\displaystyle f(-x)}$ by substituting ${\displaystyle -x}$ for all occurrence of ${\displaystyle x}$ in ${\displaystyle f\left(x\right)}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -x}$.

Rewrite ${\displaystyle -1}$ as ${\displaystyle -1\left(1\right)}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -\left(x\right)-1\left(1\right)}$.

Rewrite ${\displaystyle -(x+1)}$ as ${\displaystyle -1(x+1)}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -x}$.

Rewrite ${\displaystyle 2}$ as ${\displaystyle -1(-2)}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -\left(x\right)-1(-2)}$.

Simplify the expression.

Factor ${\displaystyle -1}$ out of ${\displaystyle -x}$.

Rewrite ${\displaystyle -6}$ as ${\displaystyle -1\left(6\right)}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -\left(x\right)-1\left(6\right)}$.

Rewrite negatives.

Check if ${\displaystyle f(-x)=f\left(x\right)}$.

Since ${\displaystyle -\frac{(x+1)(x-2)}{x+6}}$${\displaystyle \ne }$${\displaystyle \frac{(x-1)(x+2)}{x-6}}$, the function is not even.

Multiply ${\displaystyle -1}$ by ${\displaystyle \frac{(x-1)(x+2)}{x-6}}$.

Since ${\displaystyle -\frac{(x+1)(x-2)}{x+6}}$${\displaystyle \ne }$${\displaystyle -\frac{(x-1)(x+2)}{x-6}}$, the function is not odd.