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sloppycanada

  • one year ago

How to solve rational function

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  1. sloppycanada
    • one year ago
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    |dw:1435654672339:dw|

  2. amoodarya
    • one year ago
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    multiply both side by (3*4) to make it simpler

  3. sloppycanada
    • one year ago
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    Soo.. x-4+x = 72?

  4. sloppycanada
    • one year ago
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    2x = 76 x = 38

  5. amoodarya
    • one year ago
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    no this is not correct!

  6. amoodarya
    • one year ago
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    denominators are different

  7. kropot72
    • one year ago
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    Not so. Multiplying both sides by 12 gives us: \[\large \frac{12(x-4)}{4}+\frac{12x}{3}=72\]

  8. kropot72
    • one year ago
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    Which simplifies to: \[\large 3x-12+4x=72\]

  9. sloppycanada
    • one year ago
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    7x = 84

  10. kropot72
    • one year ago
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    Correct. Now find the value of x.

  11. sloppycanada
    • one year ago
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    x = 14

  12. kropot72
    • one year ago
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    Not so. What is the value of 84/7 ?

  13. sloppycanada
    • one year ago
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    Sorry 12.

  14. kropot72
    • one year ago
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    Correct.

  15. sloppycanada
    • one year ago
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    |dw:1435656598968:dw|

  16. amoodarya
    • one year ago
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    \[\frac{5x+1}{x}<1 \\\frac{5x+1}{x}-1<0 \\\frac{5x+1}{x}-\frac{x}{x}<0 \]

  17. amoodarya
    • one year ago
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    now go on

  18. sloppycanada
    • one year ago
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    Multiply both sides by "x"?

  19. amoodarya
    • one year ago
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    no no no

  20. amoodarya
    • one year ago
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    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
    • one year ago
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    \[5x+1<x \\5x-x<-1\\4x<-1\\x<-\frac{1}{4}\] but it is incomplete

  22. amoodarya
    • one year ago
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    \[\frac{4x+1}{x}<0\] |dw:1435665521336:dw|

  23. amoodarya
    • one year ago
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    \[first \space suppose \space x>0 \\\frac{5x+1}{x}<0 \rightarrow 5x+1<x \\4x<-1\\x<\frac{-1}{4}\\ now\\x>o ,x<\frac{-1}{4} \] for the second part note that sign will change \[x<0 \\\frac{5x+1}{x}<1 \\mutilply \space by -x\\5x+1>x\\4x>-1\\x>\frac{-1}{4}\\now\\x>\frac{-1}{4} ,x<0 \rightarrow \frac{-1}{4}<x<0\]

  24. sloppycanada
    • one year ago
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    That makes no sense to me...

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