Suppose $a$ and $b$ are integers in the ratio $6:7$, what is the ratio of $(6a^{2} + 7b^{2} + 6a + 7b ) : (a^{2}+b^2)$? Initially I thought I can assume $a=6$ and $b=7$ and calculate the ratio of the given expression which turned out to be $\frac{644}{85}$ and this was not the correct answer provided for this question.
Then when I turned to the solution for this problem, this statement was written as part of the solution

The degree of all the terms in the numerator is not equal and hence, the resultant ratio can't be computed.

I couldn't understand this statement. What does it mean? What's the theory behind this? I am just a little confused here and I am sorry if this question looks foolish but a little guidance will be helpful.

The integers $6$ and $7$ are in a ratio $6:7$, and plugging them in yields a ratio $644:85$. The integers $-6$ and $-7$ are also in a ratio $6:7$, and plugging them yields a ratio $474:85$. These two ratios are clearly not the same, so the ratio is not determined by the ratio of $a$ and $b$. It is a trick question.
