Melody

You want more hints ... ok

\(\frac{x - 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\\ \frac{x - 7}{x^2 - x - 2} = \frac{A(x+1)}{(x - 2)(x+1)} + \frac{B(x-2)}{(x + 1)(x-2)} \)

I answered this qeustion a short time ago.

anyway...

Add the fractions on the right side (get a common denominator first). Then equate coefficients.

let

\(x=Z+\delta\qquad \text{where Z is an integer and }0\le\delta<1\)

\(\lceil x \rceil+\lfloor x \rfloor + x = Z+1+Z+Z+\delta\\ 3Z+\delta+1=4.8\)

and you can finish it.   Remember that Z is an integer and delta is between 0 and 1

answered

Answered.

C-7=3/4(P+7)

4(c-7)=3(P+7)

4C-28=3P+21

4C-3P=21+28

4C-3P=49       (1)

C-27=1/3(P+27)

3C-81=P+27

3C-P=108       (2)

check what I have done and then solve simultaneously.     

On the right-hand side make the denominator (x-2)(x+1) 

Then the bottoms will be the same and you can just equate the coefficients on the top.

Use the quadratic formula to solve it.

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)