MHB Evaluate Fraction: Simplify $\frac {x^2 + 1 - 1}{x^2 + 1}$

[tmt1]

I have this expression:

$\frac {x^2 + 1 - 1}{x^2 + 1}$

Is there a way to simplify this expression and get:

$1 - \frac {1}{x^2 + 1}$

My professor wrote it on the board and I didn't follow the reasoning.

 

[MarkFL]

Re: Evaluating a fracion

Yes, with rational expressions, we may write:

$$\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$$

And so what your professor did can be reasoned as follows:

$$\frac{x^2+1-1}{x^2+1}=\frac{x^2+1}{x^2+1}-\frac{1}{x^2+1}=1-\frac{1}{x^2+1}$$

Does that make sense?

 

[tmt1]

Re: Evaluating a fracion

Yes, with rational expressions, we may write:

$$\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$$

And so what your professor did can be reasoned as follows:

$$\frac{x^2+1-1}{x^2+1}=\frac{x^2+1}{x^2+1}-\frac{1}{x^2+1}=1-\frac{1}{x^2+1}$$

Does that make sense?

Ah I see now, thank you