Rel language
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This site ranks well in the States and Austraila. Would rel language tags help with search for both states? https://www.dinkleboo.com/
Separating duplicate content.
Or how would you go about increasing ranking? The site ranks higher in the states than Austrailia but they want to increase their presence in AU.
US Position 4.9k
AU Position 1.3
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Howdy.
Hmm.. Hreflang is for telling google that there is the same article/page/post, just in different language. It doesn't really have much to do with actual rankings, unless you already have bunch of duplicate content. Since you said you are separating duplicate content, there shouldn't be any issues (btw, what exactly do you mean by "Separating duplicate content"?).
As for rankings improvements - SEO, links, competitions research etc. Most likely the reason of ranking lower in AU due to AU competition. Or are the competitors who are outranking you in AU are the same as the ones which are not outranking you is US?