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*PLEASE NEED HELP* (50 POINTS)

Find (f/g)(x)

f(x)= sqrt(x^2-1)

g(x)= sqrt(x-1)
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a) sqrt(x+1)

b) sqrt(x-1)

c) sqrt((-x^2)/(-x+1))

d) sqrt((1)/(x+1))

Respuesta :

keeping in mind that 

1² = 1
1³ = 1
1⁴ = 1
1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1

then

[tex]\bf \begin{cases} f(x)&=\sqrt{x^2-1}\\ g(x)&=\sqrt{x-1}\\ \left( \frac{f}{g} \right)(x)&=\frac{f(x)}{g(x)} \end{cases} \\\\\\ \cfrac{f(x)}{g(x)}\implies \cfrac{\sqrt{x^2-1}}{\sqrt{x-1}}\implies \sqrt{\cfrac{x^2-1}{x-1}}\implies \sqrt{\cfrac{x^2-1^2}{x-1}} \\\\\\ \sqrt{\cfrac{\stackrel{\textit{difference of squares}}{\underline{(x-1)}(x+1)}}{\underline{x-1}}}\implies \sqrt{x+1}[/tex]

Answer:

points...............

Step-by-step explanation:

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