# How do you evaluate a(2(a^2-a)-a(a(a+1)/(a^2+a))-(-a)^2-(a^2-a)/(a(a-1)))?

Oct 22, 2017

$= a \left({a}^{2} - 3 a - 1\right) = {a}^{3} - 3 {a}^{2} - a$

#### Explanation:

We will simplify term by term and then combine them.

(2(a^2-a) = 2a ^2 - 2a color (white)(aaa) (1)

a(a ((a+1) / (a^2+a) ) = a ( a( cancel (a + 1) / (a cancel(a+ 1))))
$= \frac{a \cdot \cancel{a}}{\cancel{a}} = a \textcolor{w h i t e}{a a a} \left(2\right)$

${\left(- a\right)}^{2} = {a}^{2} \textcolor{w h i t e}{a a a} \left(3\right)$

$\frac{{a}^{2} - a}{a \left(a - 1\right)} = \frac{\cancel{a \left(a - 1\right)}}{\cancel{a \left(a - 1\right)}} = 1 \textcolor{w h i t e}{a a a}$(4)

Combining all the terms,

$a \left(2 {a}^{2} - 2 a - a - {a}^{2} - 1\right)$

$= a \left({a}^{2} - 3 a - 1\right)$

$= {a}^{3} - 3 {a}^{2} - a$