How do you express $\frac{x^{2}}{x^{2} + x + 2}$ $x^2/(x^2 + x +2)$ in partial fractions?

Question

How do you express $\frac{x^{2}}{x^{2} + x + 2}$ $x^2/(x^2 + x +2)$ in partial fractions?

1 Answer

Impact of this question

21898 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-15T08:14:28

Partial fractions of $\frac{x^{2}}{x^{2} + x + 2}$ $x^2/(x^2+x+2)$ are $1 - \frac{x + 2}{x^{2} + x + 2}$ $1-(x+2)/(x^2+x+2$

Explanation:

As the denominator $x^{2} + x + 2$ $x^2+x+2$ is quadratic and its determinant $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $(-b+-sqrt(b^2-4ac))/(2a)$ is not rational (as $\sqrt{b^{2} - 4 a c} = \sqrt{- 7}$ $sqrt(b^2-4ac)=sqrt(-7)$ is not rational), its partial fractions will be of type $\frac{A x + B}{x^{2} + x + 2}$ $(Ax+B)/(x^2+x+2)$ .

But, degree of numerator is $2$ $2$ hence let us write $\frac{x^{2}}{x^{2} + x + 2}$ $x^2/(x^2+x+2)$ as

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

Hence partial fractions of $\frac{x^{2}}{x^{2} + x + 2}$ $x^2/(x^2+x+2)$ are $1 - \frac{x + 2}{x^{2} + x + 2}$ $1-(x+2)/(x^2+x+2$

Science

Math

Humanities

... and beyond

How do you express $\frac{x^{2}}{x^{2} + x + 2}$ $x^2/(x^2 + x +2)$ in partial fractions?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you express x2x2+x+2x^2/(x^2 + x +2) in partial fractions?

1 Answer

Explanation:

Related questions

Impact of this question

How do you express $\frac{x^{2}}{x^{2} + x + 2}$ $x^2/(x^2 + x +2)$ in partial fractions?