设a，b，c∈R₊，且abc=1，求$\frac{1}{a^2\left(b+c\right)}$+$\frac{1}{b^2\left(c+a\right)}$+$\frac{1}{c^2\left(a+b\right)}$的最小值．

语法填空

    Learning any language ____(take) practice － lots of practice! Often, it's difficult to know ____ you should practice it. Should you watch a video? Perhaps,____ would be a good idea to do a few quizzes. Of course, you should try to speak English with your friends. All of these are great ideas, but it's also important to build a routine. A routine will help you make ____ (study) English a habit. That's the best way to improve your English!

    It's important to ____ (expose) to many different areas every day.____, you shouldn't try to study too many ____ (differ) subjects. These suggestions take a 30-minute listening and reading as the basis for daily practice. You are trying to learn many new things, so don't try to learn too much in any one area too ____ (quick)! 

    Take 5 minutes to write down all the new words you find in your listening and reading exercises. Keep a notebook, and write in the ____ (translate) in your native language. Don't forget to learn grammar for 10 minutes. Try to quickly summarize what you listened to and what you read and speak out loud.

    That's it! Approximately 45 minutes a day, every day or at least four times a week! If you continue to do this, you will be ____ (surprise) at how quickly your English improves!