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# Can somebody explain why the numerator is being divided?

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- Steve ALv 77 months ago
As x approaches infinity, the numerator approaches 2x while the denominator approaches 4x

2x/4x = 1/2 as a limit

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- TomVLv 77 months ago
If you divide the denominator by x, you must also divide the numerator by x to avoid changing the expression. Since x = √x², dividing the numerator by √x² is equivalent to dividing by x.

It says "Divide sides by x = √x²". In this case the "sides" are actually numerator and denominator.

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- ted sLv 77 months ago
really it should have been √(4x²+ 4x) = x √(4 + 4 / x) & 4x + 1 = x ( 4 + 1 / x)...then the factor ' x > 0 ' is in both and can be cancelled to get lim { x ---> ∞ } √(4 + 4 / x) / ( 4 + 1/x) ----> 2 / 4 = 1 /2

- TomVLv 77 months agoReport
Which is the exact equivalent of dividing both numerator and denominator by x

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