Question

Find the sum: x-2/x^2+1 + x+3/x^2+1

Answer 1

To sum the two fractions (x - 2)/(x² + 1) and (x + 3)/(x² + 1), combine the numerators to get (2x + 1)/(x² + 1), which is the simplified form.

Step-by-step explanation:

You have been asked to find the sum of two fractions with the same denominator:

• (x - 2)/(x² + 1) + (x + 3)/(x² + 1)

To add these fractions, you simply combine the numerators since the denominators are identical:

• (x - 2 + x + 3)/(x²+ 1)

We can further simplify the numerator by adding the like terms:

• (2x + 1)/(x² + 1)

This is the simplified form of the sum of the two fractions.

Answer 2

For this case we have the following expression:

`\frac {x-2} {x ^ 2 + 1} + \frac {x + 3} {x ^ 2 + 1}`

We observe that both fractions have the same denominator. Therefore, we add the numerators.

We have then:

`\frac {(x-2) + (x + 3)} {x ^ 2 + 1}`

Then, rewriting the expression we have:

`\frac {2x + 1} {x ^ 2 + 1}`

Answer:

The equivalent expression is given by:

`\frac {2x + 1} {x ^ 2 + 1}`