How do you express $\frac{x^{3}}{x (x^{2} + 2 x + 1)}$ $x^3/[x(x^2+2x+1)]$ in partial fractions?

Question

How do you express $\frac{x^{3}}{x (x^{2} + 2 x + 1)}$ $x^3/[x(x^2+2x+1)]$ in partial fractions?

1 Answer

Related questions

What does partial-fraction decomposition mean?
What is the partial-fraction decomposition of $\frac{5 x + 7}{x^{2} + 4 x - 5}$ $(5x+7)/(x^2+4x-5)$ ?
What is the partial-fraction decomposition of $\frac{x + 11}{(x + 3) (x - 5)}$ $(x+11)/((x+3)(x-5))$ ?
What is the partial-fraction decomposition of $\frac{x^{2} + 2 x + 7}{x {(x - 1)}^{2}}$ $(x^2+2x+7)/(x(x-1)^2)$ ?
How do you write $\frac{2}{x^{3} - x^{2}}$ $2/(x^3-x^2)$ as a partial fraction decomposition?
How do you write $\frac{x^{4}}{{(x - 1)}^{3}}$ $x^4/(x-1)^3$ as a partial fraction decomposition?
How do you write $\frac{3 x}{(x + 2) (x - 1)}$ $(3x)/((x + 2)(x - 1))$ as a partial fraction decomposition?
How do you write the partial fraction decomposition of the rational expression $\frac{x^{2}}{x^{2} + x + 4}$ $x^2/ (x^2+x+4)$ ?
How do you write the partial fraction decomposition of the rational expression # (3x^2 + 12x -...
How do you write the partial fraction decomposition of the rational expression $\frac{1}{(x + 6) (x^{2} + 3)}$ $1/((x+6)(x^2+3))$ ?

Impact of this question

1614 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-13T05:42:01

$\frac{x^{3}}{x (x^{2} + 2 x + 1)} = 1 - \frac{2}{x + 1} + \frac{1}{{(x + 1)}^{2}}$ $x^3/(x(x^2+2x+1))=1-2/(x+1)+1/(x+1)^2$

Explanation:

This one is relatively simpler and need for detailed solution as given here, does not arise.

$\frac{x^{3}}{x (x^{2} + 2 x + 1)} = \frac{x^{2}}{x^{2} + 2 x + 1} = \frac{x^{2} + 2 x + 1 - (2 x + 1)}{x^{2} + 2 x + 1}$ $x^3/(x(x^2+2x+1))=x^2/(x^2+2x+1)=(x^2+2x+1-(2x+1))/(x^2+2x+1)$

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

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

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

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

Science

Math

Humanities

... and beyond

How do you express $\frac{x^{3}}{x (x^{2} + 2 x + 1)}$ $x^3/[x(x^2+2x+1)]$ in partial fractions?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you express x^3/[x(x^2+2x+1)]x3x(x2+2x+1)x^3/[x(x^2+2x+1)] in partial fractions?

1 Answer

Explanation:

Related questions

Impact of this question

How do you express $\frac{x^{3}}{x (x^{2} + 2 x + 1)}$ $x^3/[x(x^2+2x+1)]$ in partial fractions?