Left Panel
The first thing you must do is expand q(x). That means you multiply the two brackets together. When you do that, you get
Q(x) = x^5 + 2x^4 - 2x^3 - x^2 - 6.
Now and only now can you begin to look at what the answer might be. The largest power of x is still x^5 which means that you are not multiplying and it is doubtful that you are dividing. So C is incorrect.
You are not offered a division so we can put that thought in moth balls. Q(x) has an 2x^4 power in it, but the answer has only x^4 so you must be subtracting. That means that A is incorrect. p - q won't work because the x^5 would become negative. So B is gone.
ABC are all gone. That means D is the answer.
x^5 is plus. x^4 is a single and came about because 2x^4 - x^4 =x^4. Although it is a little risky, we need go no further
D:Answer.
Middle Panel
The common denominator is 2x(x-2) when you look at the denominator of the left fraction. You have used the distributive property to pull that 2x outside the brackets. The fraction on the right adds nothing to the denominator. The LCD is 2x(x - 2)
To put everything over that common denominator, your fraction would look like this
1/(2x(x - 2)) - 1*2*2(x - 2)/2x(x-2)
So now we get
1 - 4(x - 2)
========
2x(x - 2)
(1 - 4x + 8)
============
2x(x - 2)
(9 - 4x) / (2x(x - 2)
(-4x + 9)/ (2x(x - 2)) which is A
Right Panel
I don't trust my battery and I'm not at home I have to be really scant on this. I'll start from the Left and going down. The top one if C or third from the left.
The second one down is A, first one on the left.
The third one down is B, which is the second one on the top left.
And the last one is D, last one from the left matched with the bottom one.
The first one going down is
(x^2 - 4x + 10)/(x - 2)
The Second One down is
(x^2 + x + 4)/(x - 2)
Third down
(x^2 - x + 4) / (x - 2)
Fourth down
(x^2 - 5x + 16) / (x - 2)
