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## Main Question or Discussion Point

I was hoping someone could clarify a step of an example in my calculus textbook.

lim x→∞ (√(2*x

The description for the step says to divide numerator and denominator by x.

I understand to divide top and bottom of a rational function by the x

lim x→∞ (√(2*x

^{2}+1))/(3*x-5) = lim x→∞ (√(2+(1/x^{2})))/(3-(5/x)), (since √x^{2}=x for x>0)The description for the step says to divide numerator and denominator by x.

I understand to divide top and bottom of a rational function by the x

^{n}where n is the highest power of x that occurs in the denominator in this situation but I don't understand how the numerators equate in this equation.