Question

How to simplify this expression ?

Answer 1

Answer:

$\large \boxed{\sf \ \ \dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{2x+1}{x^2(x+1)} \ \ }$

Step-by-step explanation:

Hello,

This is the same method as computing for instance:

$\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{3+2}{2*3}=\dfrac{5}{6}$

We need to find the same denominator.

Let's do it !

For any x real different from 0, we can write:

$\dfrac{1}{x^2}+\dfrac{1}{x^2+x}=\dfrac{1}{x^2}+\dfrac{1}{x(x+1)}\\\\=\dfrac{x+1+x}{x^2(x+1)}=\dfrac{2x+1}{x^2(x+1)}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you