Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

What number comes next in this sequence:
7 8 5 5 3 4 4 _

Two friends were stuck in a cottage. They had nothing to do and thus they started playing cards. Suddenly the power went off and Friend 1 inverted the position of 15 cards in the normal deck of 52 cards and shuffled it. Now he asked Friend 2 to divide the cards into two piles (need not be equal) with equal number of cards facing up. The room was quite dark and Friend 2 could not see the cards. He thinks for a while and then divides the cards in two piles.

On checking, the count of cards facing up is same in both the piles. How could Friend 2 have done it ?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

One night, a woman receives a call from the police. They tell her that her husband was murdered and that she should come to the crime scene as soon as possible. The woman drops the phone, shocked, and drives 20 minutes to the crime scene. As soon as she reaches the crime scene, the police arrest her and she is convicted of murder. How do the police know she committed the crime?

All of you like to eat me. I am a five-lettered word. Remove the first two and I turn into an infamous animal. Remove just the first and I become a heinous crime. Remove the first and the last and you can groove on me.

Can you guess who am I?

Solve the equation in the image by looking at the pattern closely.

Here is a mathematical expression that also secretly tells a movie name. What movie is that?

There is a place where if I stand up straight, I will still be considered sideways.