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# C3 intro

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1. I'm really struggling with fractions does anyone have any tips on how to solve this question:
2. No question showing up for me...
3. Hang on let me type it out looks like it didn't work first time round ☺️
4. So, f(x)= 1- 3/(x+2) + 3/(x+2)^2 where x\= -2

Show that f(x) = (x^2+x+1)/ (x+2)^2
5. Then part b) and c) is also a bit hazy for me too

B) Show that x^2+ x+1>O for all values of x

C) show that f(x) >O for all values of x.
6. (Original post by Trudy9)
So, f(x)= 1- 3/(x+2) + 3/(x+2)^2 where x\= -2

Show that f(x) = (x^2+x+1)/ (x+2)^2
You want to make the denominators the same. The highest denominator you have is (X+2)^2, so you need to multiply 1 by (x+2)^2 and then multiply -3 by (x+2) and then keep the last bit as it is...
7. (Original post by Trudy9)
x
Remember that to add fractions, they must have the same denominator, so you can cross multiply as necessary to make sure that they have the same denominator.

Eg (1/2) + (1/3) is given a common denominator 6 by 'multiplying' the first by 3 and the second by 2 to give (3/6) + (2/6) = (5/6). Yours already has the common factor of (x+2) so it is not as confusing, but you apply similar logic.
8. (Original post by Trudy9)
Then part b) and c) is also a bit hazy for me too

B) Show that x^2+ x+1>O for all values of x

C) show that f(x) >O for all values of x.
part b is showing that f(x) is an increasing function, so you need to differentiate the function and show that it is always positive !
9. (Original post by fefssdf)
part b is showing that f(x) is an increasing function, so you need to differentiate the function and show that it is always positive !
No it isn't - it's showing that the function is > 0 for all x. That's completely different from showing that a function is increasing! There's no differentiation required in this question
10. (Original post by Trudy9)
B) Show that x^2+ x+1>O for all values of x
Think about completing the square. What can you say about (number)^2 + (positive number)? Is that always positive, is it always negative is it what...?

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