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## Homework Statement

Hello,

I know the direct substitution property in calculus. But, the definition of a rational function still confuses me.

For example, are these rational functions:

y=(x^2+2x+1)/(x+1)

y=((x^2+2)^(1/2))/(x+1)

The denominator of the first one could cancel. So, is there still a ratio? Is it a rational function?

The second one has a root in the numerator. The exponents of are not integers. Is it still a rational function?

Please help me. I do not understand the definition.