The first time I tried this problem I found it challenging because I had never attempted to solve an equation by adding two fractioned radicals without the help of a peer or teacher. The whole concept of working with radicals by themselves was still new to me so adding fractions to the equation made it a bit more challenging to solve.
During my first attempt at solving this equation, I was able to factor out numbers from the numerators and also the “x2” in the denominator of the second fraction. However, I got stuck when I had to make the denominators the same before adding the fractions together. This was quite a simple step that I had learned previously but forgot to do; in order to add fractions, the denominator must be the same – you can multiply the denominator and numerator by a common multiple so that both denominators from each fraction are the same. After completing and understanding this step, I made another mistake by adding both the coefficients in the numerator as well as the radicands in the numerators. This step is incorrect and led me to a false answer as when you add the same radicals with coefficients, you only add the coefficients and must keep the radials and radicands the same. This is because if a radical has the same index and radicand, you can add or subtract as normal. However, if they were different, you cannot add or subtract.
To find the correct solution and solve this question properly, I used a variety of resources. First, I reviewed my notes with my peers so we could all understand and figure it out together. The notes did help show where I went wrong, but I also consulted with my math tutor so she could fully explain why I was wrong and why the correct steps make more sense (more description).
In order to remember how to solve this equation, the concepts/skills I needed were that when you add fractions with radicals, you first need to make the denominators the same (by using common multiples). In addition, I needed to remember that when you add the radicals together, if they have the same radicand, all you do is add the coefficients.
Next time I encounter a difficult problem, I might try to use other strategies such as use the answer key to work backwards or watch a video on YouTube so someone can explain the steps to me and the reasoning behind them. All in all, I feel that the strategies I used to solve this challenging question were useful, helped me get the correct answer, and made me learn from my mistakes.
