## sloppycanada one year ago How to solve rational function

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2. amoodarya

multiply both side by (3*4) to make it simpler

Soo.. x-4+x = 72?

2x = 76 x = 38

5. amoodarya

no this is not correct!

6. amoodarya

denominators are different

7. kropot72

Not so. Multiplying both sides by 12 gives us: $\large \frac{12(x-4)}{4}+\frac{12x}{3}=72$

8. kropot72

Which simplifies to: $\large 3x-12+4x=72$

7x = 84

10. kropot72

Correct. Now find the value of x.

x = 14

12. kropot72

Not so. What is the value of 84/7 ?

Sorry 12.

14. kropot72

Correct.

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16. amoodarya

$\frac{5x+1}{x}<1 \\\frac{5x+1}{x}-1<0 \\\frac{5x+1}{x}-\frac{x}{x}<0$

17. amoodarya

now go on

Multiply both sides by "x"?

19. amoodarya

no no no

20. amoodarya

if you are sure that "x>0" you can multiply by "x" but in this case we can not be sure about x>0 if you do it by multiply ,some part of answer is lost !

21. amoodarya

$5x+1<x \\5x-x<-1\\4x<-1\\x<-\frac{1}{4}$ but it is incomplete

22. amoodarya

$\frac{4x+1}{x}<0$ |dw:1435665521336:dw|

23. amoodarya

$first \space suppose \space x>0 \\\frac{5x+1}{x}<0 \rightarrow 5x+1<x \\4x<-1\\x<\frac{-1}{4}\\ now\\x>o ,x<\frac{-1}{4}$ for the second part note that sign will change $x<0 \\\frac{5x+1}{x}<1 \\mutilply \space by -x\\5x+1>x\\4x>-1\\x>\frac{-1}{4}\\now\\x>\frac{-1}{4} ,x<0 \rightarrow \frac{-1}{4}<x<0$