# Thread: How do I simplify this expression?

1. ## How do I simplify this expression?

Okay, so I need step by step on how to simplify this expression:
(a + 2) / (a^2 + a) ÷ (a + 2) / (a^3)

2. Originally Posted by jenbones
Okay, so I need step by step on how to simplify this expression:
(a + 2) / (a^2 + a) ÷ (a + 2) / (a^3)

That is the same as $\displaystyle \frac{a+ 2}{a^2+ 2}\frac{a^3}{a+ 2}$ (because, as we learned in the third grade, to divide fractions, we invert the divisor and multiply). Now, what can you cancel?

3. cancel out the a + 2

$\displaystyle \frac{(a + 2)}{(a^2 + a)}:\frac{(a + 2)}{(a^3)} = \frac{(a + 2)}{(a^2 + a)}\cdot \frac{(a^3)}{(a+2)} = \frac{(a ^3)}{(a^2+a)} = \frac{(a ^3)}{a(a+1)} = \frac{(a ^2)}{(a+1)} \ \ \ \ \$

5. are you sure the answer is (a^3) / (a^2 + 2) ? I know for a fact the answer is (a^2) / (a + 1)

Never mind, I see.

6. the two brackets (a+2) will cancel out each other to give...

(1 / (a^2 + a)) ÷ (1/(a^3)

then if we multiply both the top line and the bottom line by a^3 then the (1/(a^3)) bit we originally have will disappear as
a^3/a^3 is 1

multiply (1 / (a^2 + a)) by a^3 we get (a^3)/(a^2 + a)

this is effectively turning the divisor upside down and multiplying.

now (a^2 + a) can be factorised into what...?