what to solve firsti have 2 fractions (x+1)/(x^2+1)+(2x-2)/(x^2+1) i don't understand why to write separate and not combined how to solve

Asked on by for3cast

2 Answers | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

Depending on the situation, you may use this way to write a fraction, whose denominator is a polynomial.

If you need to solve an indefinite integral, splitting the fraction may help you to solve more but easier indefinite integrals.

In this case, the original numerator may be evaluated such that:

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

It is a way to show that a fraction could be written as a sum of 2 or more fractions, depending on the number of terms from numerator.

In this case, the problem combined 2 terms from the total of 4 terms. In this way, we can add 2 fractions that have the same denominator.

Also the fraction could be written as an algebraic sum of 4 terms.

x/(x^2+1) + 1/(x^2+1) + 2x/(x^2+1) - 2/(x^2+1)

Since the denominators are common, we'll write:

(x + 1 + 2x - 2)/(x^2+1)

We'll combine like terms and we'll get the result:

(3x - 1)/(x^2+1)

We’ve answered 319,647 questions. We can answer yours, too.

Ask a question