# Lim x→inf text book example confusing step

1. Sep 10, 2012

### cambo86

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

lim x→∞ (√(2*x2+1))/(3*x-5) = lim x→∞ (√(2+(1/x2)))/(3-(5/x)), (since √x2=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 xn 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.

2. Sep 10, 2012

### Stephen Tashi

For x > 0, (1/x) sqrt( 2x^2 + 1) = sqrt(1/x^2) sqrt(2x^2 + 1) = sqrt( (1/x^2)(2x^2 + 1) )