MarkFL said:Yes, with rational expressions, we may write:
\(\displaystyle \frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}\)
And so what your professor did can be reasoned as follows:
\(\displaystyle \frac{x^2+1-1}{x^2+1}=\frac{x^2+1}{x^2+1}-\frac{1}{x^2+1}=1-\frac{1}{x^2+1}\)
Does that make sense?
Simplifying a fraction helps to make it easier to work with and understand. It also allows you to see the relationship between the numerator and denominator more clearly.
To simplify this fraction, you can factor out any common factors in the numerator and denominator. In this case, both the numerator and denominator have a common factor of (x^2 + 1), so they can be cancelled out, leaving the simplified form of 1.
No, fractions cannot be simplified to zero. However, they can be simplified to a fraction with a numerator of zero, which is equivalent to the value of zero.
Yes, simplifying a fraction and reducing it are essentially the same thing. Both processes involve finding the simplest form of a fraction by cancelling out common factors in the numerator and denominator.
No, this fraction is already in its simplest form and cannot be simplified any further.