## mathmath333 one year ago \large \color{black}{\begin{align} &\text{Find the number of integer values } \hspace{.33em}\\~\\ &\dfrac{15x^2+2x+1}{x^2-2x-1}\hspace{.33em}\\~\\ &\text{doesn't satisfy } \hspace{.33em}\\~\\ \end{align}}

1. anonymous

Hi math, Does that mean the number of integer values, which can not be written in the form:$\dfrac{15x^2+2x+1}{x^2-2x-1}$?

2. mathmath333

i mean the number of integer values the expression $$\dfrac{15x^2+2x+1}{x^2-2x-1}$$ not take

3. anonymous

aha that's right, so we just need to find the range of function

4. anonymous

$y=\dfrac{15x^2+2x+1}{x^2-2x-1}$find $$x$$ in terms of $$y$$, find the domain of inverse

5. anonymous

@mukushla exact !

6. mathmath333

what u mean by x interms of y

7. anonymous

solve the equation . and deal with y as a parameter

8. anonymous

Separate x i.e. find x = ? and replace y with x afterwards.

9. mathmath333
10. ganeshie8

Following mukushla's hint $\large y=\dfrac{15x^2+2x+1}{x^2-2x-1}$ cross multiplying and rearranging gives $\large (15-y)\color{red}{x^2}+(2+2y)\color{red}{x}+y+1 = 0$ This is a quadratic in $$\color{red}{x}$$ you may use the discriminant to find the domain

11. mathmath333

ok, d=8(y+1)(y-7)

12. ganeshie8

how?

13. mathmath333

from this -> (2+2y)^2-4(15-y)(y+1)

14. ganeshie8

Ohk.. Notice that $$D \ge 0$$ for the quadratic equation to make sense in real numbers

15. mathmath333

$$y>=7 ,y<=-1$$

16. ganeshie8

those are the values the given rational expression ever takes

17. mathmath333

18. ganeshie8

19. anonymous

no but these numbers satisfy the equation

20. mathmath333

oh ok thnx

21. anonymous

what on earth the question says does not satisfy??

22. ganeshie8

|dw:1434277279587:dw|

23. anonymous

The directions could be more clear. This might be better. "What integer values does the expression not attain. " or "What integer values does the function not attain. "

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