Question

*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))

Answer 1

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

Explanation:

Answer 2

keeping in mind that

1² = 1
1³ = 1
1⁴ = 1
1¹⁰⁰⁰⁰⁰⁰⁰⁰⁰ = 1

then


`\bf \begin{cases} f(x)&=√(x^2-1)\\ g(x)&=√(x-1)\\ \left( (f)/(g) \right)(x)&=(f(x))/(g(x)) \end{cases} \\\\\\ \cfrac{f(x)}{g(x)}\implies \cfrac{√(x^2-1)}{√(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 √(x+1)`