How to find the partial fractions for this expression?

[ybhathena]

Homework Statement

Find the partial fractions for this expression.

(((n+1)*(sqrt(n)) - n*(sqrt(n+1))) / (n*(n+1)))

The Attempt at a Solution

The final answer is 1/sqrt(n) - 1/(sqrt(n+1))

My work:

A/n - B/(n+1) = n*sqrt(n+1) - (n+1)*(sqrt(n))
I am subbing in n = -1 and n = 0 to solve for A and B which usually works but in this case it is giving me A = 0 and B = 0, which means I am getting 0 as my partial fraction. Thank you for your help.

 

[pasmith]

Homework Statement

Find the partial fractions for this expression.

(((n+1)*(sqrt(n)) - n*(sqrt(n+1))) / (n*(n+1)))

The Attempt at a Solution

The final answer is 1/sqrt(n) - 1/(sqrt(n+1))

My work:

A/n - B/(n+1) = n*sqrt(n+1) - (n+1)*(sqrt(n))
I am subbing in n = -1 and n = 0 to solve for A and B which usually works but in this case it is giving me A = 0 and B = 0, which means I am getting 0 as my partial fraction. Thank you for your help.

Your expression doesn't require partial fractions, it requires re-writing as $$\frac{(n+1)\sqrt{n} - n\sqrt{n+1}}{n(n+1)} = \frac{(n+1)\sqrt{n}}{n(n+1)} -\frac{n\sqrt{n+1}}{n(n+1)}$$ and further simplifications in each term.

 

[ybhathena]

Thank you very much !