Question

Is rationalizing a denominator is the same as multiplying by 1?

Answer 1

Answer:

Step-by-step explanation:

yes.  

Assume you have the function:

$f(x)=\frac{1}{\sqrt{x} }$

Then in order to rationalize the denominator, you'd multiply the whole function by 1:

$f(x)=\frac{1}{\sqrt{x} } *\frac{\sqrt{x} }{\sqrt{x} } =\frac{\sqrt{x} }{x\\}$

Answer 2

check the links in the comments above, notice on all those links, we multiply top and bottom always by the same value, it being the conjugate pair or just a rational or something else, is the same value atop and below.

now, what is same over same?

$\bf \cfrac{same}{same}\implies \cfrac{spaghetti}{spaghetti}\implies \cfrac{\textit{frying pan}}{\textit{frying pan}} \\\\\\ \cfrac{\sqrt{3x^3-y^4}}{\sqrt{3x^3-y^4}}\implies \cfrac{\log_5(z^e)}{\log_5(z^e)}\implies \boxed{1}$

so you see, we're really always multiplying the fraction by 1, so its top and bottom are just 1 in disguise.