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Math Help - More complex equations with fractions

  1. #1
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    More complex equations with fractions

    Can someone help explain this to me please..

    x+3/2 + x+4/3 = 2

    y+5/6 + y-1/2 = 10

    z+1/2 - z-1/4 = 1
    d+12/3 + d+3/6 = 3d + 11/2
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  2. #2
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    Hello, bronaghxo!

    I assume it's the same old complaint: "I hate fractions!"
    Unless you plan to count apples or sheep all your life,
    . . you better learn to handle them.


    Solve for x\!:\;\;x+\frac{3}{2} + x + \frac{4}{3} \:=\: 2

    Well, there's one blessing . . . With an equation, we can eliminate the fractions.


    We have: . x + \frac{3}{2} + x + \frac{4}{3} \;=\;2


    Multiply both sides by the LCD (6):

    . . 6\,\bigg[x + \frac{3}{2} + x + \frac{4}{3}\bigg] \;=\;6\,\bigg[2\bigg]

    . . 6(x) + 6\left(\frac{3}{2}\right) + 6(x) + 6\left(\frac{4}{3}\right) \:=\:6(2)

    . . 6x + 9 + 6x + 8 \:=\:12 \quad\Rightarrow\quad 12x + 17 \:=\:12 \quad\Rightarrow\quad 12x \:=\:-5


    Therefore: . x \:=\:-\frac{5}{12}

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  3. #3
    MHF Contributor red_dog's Avatar
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    \frac{x+3}{2}+\frac{x+4}{3}=2
    The common denominator is 6. So amplify the first fraction with 3 and the second with 2 and the right hand member with 6

    3(x+3)+2(x+4)=12\Leftrightarrow 5x=-5\Leftrightarrow x=-1


    Try to solve the others equations in the same manner.
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