Evaluating $\lim_{x\to1^+}\frac{\sqrt{x+1}+\sqrt{x^2 -1}-\sqrt{x^3+1}}{\sqrt{x-1}+\sqrt{x^2 +1}-\sqrt{x^4+1}}.$ I don't know how to solve these kind of limit problems. I was wondering if someone could help me about it to learn them. $$\lim_{x\to 1^+}\frac{\sqrt{x+1}+\sqrt{x^2 -1}-\sqrt{x^3+1}}{\sqrt{x-1}+\sqrt{x^2 +1}-\sqrt{x^4+1}}.$$ Thanks in advance.

Hint
You can always write $f(x)-g(x)$ as $$\frac{f(x)^2-g(x)^2}{f(x)+g(x)}.$$
So, taking $$f(x)=\sqrt{x+1}+\sqrt{x^2+1}\quad \text{and}\quad g(x)=\sqrt{x^3+1},$$ at the numerator and $$f(x)=\sqrt{x-1}+\sqrt{x^2+1}\quad \text{and}\quad g(x)=\sqrt{x^4+1},$$
at the denominator should do the work.
