Answer:Hence choice A is correct Step-by-step explanation:Given equations are [tex]f(x)=\sqrt{x^2-1}[/tex] and [tex]g(x)=\sqrt{x-1}[/tex]Now we need to find the value of [tex]\left(\frac{f}{g}\right)\left(x\right)[/tex]. Then select correct matching choice from the given choices. Now let's find [tex](fof)(3)[/tex][tex]\left(\frac{f}{g}\right)\left(x\right)[/tex][tex]\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}[/tex][tex]\left(\frac{f}{g}\right)\left(x\right)=\frac{\sqrt{x^2-1}}{\sqrt{x-1}}[/tex][tex]\left(\frac{f}{g}\right)\left(x\right)=\frac{\sqrt{\left(x+1\right)\left(x-1\right)}}{\sqrt{x-1}}[/tex][tex]\left(\frac{f}{g}\right)\left(x\right)=\sqrt{x+1}[/tex]Hence choice A is correct