Little question

Is it possible to beat a website which is about 3 years older and if yes, how?
There is a website for which I did SEO while I was working for that company, and have managed to rank it on the top positions in google.
Now I have my own business with the same thematic, and have my own website, which is ranked highly, but it seems that I can't beat the previous one... Is there any way in the world to succeed in that???

Well of course there are ways to do it, but what kind of time frame are you looking at? Where do you rank now? What budget do you have to do it? Just a couple questions, but it would help us answer your question better

It's totally possible, but it'll be harder than positioning the other website.

PS : you're trying to "beat yourself" on this, nice challenge

Tons of backlinks
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Thanks for the replies.
It is frustrating to pay for the SEO, since I've never done that for the old website.
We're talking about website in Serbian language and there was no some seriouse competition back then, but seems I became my own competition.
Yeah, nice challenge I would have to buy some links, since it looks like the easiest way.
Regarding the positions, the old website is on the 2d place first page, and my the 9th place first page, sometimes it's only 2-3 places difference, rarely, the difference is 2-3 pages.
Thank you all again