Answer:
The function is equivalent to
[tex]\frac{x+1}{x^3-x}=\frac{1}{x\left(x-1\right)}[/tex]
Step-by-step explanation:
Given the function
[tex]f\left(x\right)=\frac{x+1}{x^3-x}[/tex]
Let us simplify this function
[tex]f\left(x\right)=\frac{x+1}{x^3-x}[/tex]
[tex]=\frac{x+1}{x\left(x+1\right)\left(x-1\right)}[/tex] ∵ [tex]Factor\:x^3-x=x\left(x+1\right)\left(x-1\right)[/tex]
Cancel the common factor (x+1)
[tex]=\frac{1}{x\left(x-1\right)}[/tex]
Therefore, the function is equivalent to
[tex]\frac{x+1}{x^3-x}=\frac{1}{x\left(x-1\right)}[/tex]
