I need help for some super basic questions ;_;

[pikachuuu77]

I'd like working out shown with the answers too. I don't understand these specific questions and I'm just at my wits ends. Any help would be greatly appreciated.

Q1) Simplify, expressing the answer with a rational denominator
1/√(x-1) - √(x-1)

Q2) Simplify fully
1/x-1 - 1/x+1 + 1

Q3) Re-arrange for r
1/f = 1/s + 1/r

Q4) Illustrate the set (-3, ∞) n ( not an actual n, that n like shape - can't type it on this keyboard, can't remember what it is either. :/ ) ( -∞, 5] on a number line

Q5) P(x) = 2x^2 + 3ax + 7 is divisible by (x+1) the remainder is 3. Find the value of a.

Q6) Solve the inequality 8^n-2 > 2048

That's all.

* I posted this on Yahoo answers but no one has replied so - yeah.
Please atarnotes peeps. I'd send anyone who helps me a buffet if I could ;_;

[keltingmeith]

Essentially, the way to do the first three questions, is to:

1. Multiply all the denominators out. (numbers, or non-letters, can be left in the denominator)
2. Multiply out all the brackets.
3. Collect like terms.
When solving, we add a few more steps:
4. Collect what you're solving for to one side of the equation. Remove everything else to the other side.
5. Factorise what you want out.
6. Divide by what's left.

1.


2.


3.


4. For this question, the "n" you're talking about is, presumably, this symbol: . This is referred to as an intersection. An intersection just takes what's in common - for example, . Reckon you can give this one a shot, now?

5. Apply the remainder theorem. If f(x)/(ax-b) has remainder r, then f(b/a)=r. Use this to set up a new quadratic equation, which should help you solve for your a.

6. This one's a bit trickier - one way is to work off the graph, here's another:

[pikachuuu77]

Essentially, the way to do the first three questions, is to:

1. Multiply all the denominators out. (numbers, or non-letters, can be left in the denominator)
2. Multiply out all the brackets.
3. Collect like terms.
When solving, we add a few more steps:
4. Collect what you're solving for to one side of the equation. Remove everything else to the other side.
5. Factorise what you want out.
6. Divide by what's left.

1.


2.


3.


4. For this question, the "n" you're talking about is, presumably, this symbol: . This is referred to as an intersection. An intersection just takes what's in common - for example, . Reckon you can give this one a shot, now?

5. Apply the remainder theorem. If f(x)/(ax-b) has remainder r, then f(b/a)=r. Use this to set up a new quadratic equation, which should help you solve for your a.

6. This one's a bit trickier - one way is to work off the graph, here's another:

THANKYOU SO MUCH! You're a lifesaver.
Greatly appreciated the worked steps too