How to solve this? Really simple!

(πa^2/2 - a^2) / 2a^2

answer should be (π-2)/4

No matter what I do, I cannot get rid of the a. Please show me how to do this and thanks in advance!

(πa^2/2 - a^2) / 2a^2

Factor out a^2 from top

((π/2 - 1)*a^2) / 2a^2

a^2 can be canceled out

(π/2 - 1)/2

Multiply by 2/2 to get rid of fraction in numerator

Answer: (π - 2)/4

One of the ways you can simplify a problem is by writing out the exponents:

( π * a * a / 2) - (a * a) / 2 * a * a

that can also be written as:

[ ( π * a * a / 2) - (a * a) ] * [ 1 / (2 * a * a) ]

Now you would multiply each "part" of [ ( π * a * a / 2) - (a * a) ] by [ 1 / (2 * a * a) ]:

( π * a * a / 2) * 1 / (2 * a * a)

If you write it out, you will notice that the 2 a's on the top of the first fraction cancel out with the 2 a's on the bottom of the second fraction. You are then left with: π / 4

(a * a) / 1 * 1 / (2 * a * a)

If you write it out, you will notice that the 2 a's on the top of the first fraction cancel out with the 2 a's on the bottom of the second fraction. You are then left with: 1 / 2

Now our equation looks like this:

(π / 4) - (1 / 2)

Now just simplify:

(π / 4) - (1 / 2)
(π / 4) - (2 / 4)
(π - 2) / 4

Answer: (π-2)/4


*It would help if you wrote out the steps described above on paper. It is easier to understand if you see it written out correctly, step-by-step.

πa²/2 – a²
---------------- = ∙ ∙ ∙ ∙ distribute the division
∙ ∙ 2a²

πa² ∙ ∙ a²
----- – ------ = ∙ ∙ ∙ ∙ ∙divide out the a² 's
4a² ∙ ∙ 2a²

π/4 – 1/2 = ∙ ∙ ∙ ∙ ∙ rewrite 1/2 to same denominators
π/4 – 2/4 = ∙ ∙ ∙ ∙ ∙ factor out the division
(π – 2) / 4

[(πa^2)/2 - a^2] / (2a^2)

Factor an a^2 from each term in the numerator and denominator:
[(π/2 - 1)/2] * a^2 / a^2

a^2 / a^2 = 1:
[(π/2 - 1)/2] * 1

Multiply everything inside the brackets by 2:
(π - 2)/4

(πa^2/2)/(2a^2/1)-(a^2)/(2a^2)
(πa^2*1)/(2*2a^2)-1/2
(πa^2)/(4a^2)-1/2
π/4-2/4
(π-2)/4