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Math Help - Simplifying

  1. #1
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    Simplifying

    Please help me isolate x

    (x-a)/b-(x+c)/d=0
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  2. #2
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    Re: Simplifying

    Do you mean \displaystyle \frac{(x - a)}{b} - \frac{(x - c)}{d} = 0?

    If so...

    \displaystyle \begin{align*} \frac{(x - a)}{b} - \frac{(x - c)}{d} &= 0 \\ \frac{(x - a)}{b} &= \frac{(x - c)}{d} \\ d(x - a) &= b(x - c)  \end{align*}

    Now expand the brackets and see what you can do from there...
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  3. #3
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    Re: Simplifying

    Yes, except it's x+c. According to my math book, the answer is x=(ad+bc)/(d-b)
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  4. #4
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    Re: Simplifying

    Your maths book would be right

    As Prove It says (with the amended (x+c):

    [(x-a)/b]-[(x+c)/d]=0

    add (x+c)/d to both sides

    (x-a)/b=(x+c)/d

    multiply top and bottom of lhs by d
    multiply top and bottom of rhs by b
    gives

    d(x-a)/bd=b(x+c)/bd

    multiplying both sides by bd gives

    d(x-a)=b(x+c)

    You should be able to complete it from there

    hth

    btw Prove It, How do you get the horizontal line for divide?

    thx

    Pro
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  5. #5
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    Re: Simplifying

    I'm sorry, but I don't get the last bit. dx-bx=ad+bc, then divide both sides with d-b? However, I still have two x:es
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  6. #6
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    Re: Simplifying

    dx-bx=ad+bc, then divide both sides with d-b?
    You're getting there

    dx-bx=ad+bc

    dx-bx is the same as x(d-b)

    so we have x(d-b)=(ad+bc)

    dividing both sides by (d-b) gives

     x=(ad+bc)/(d-b)
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  7. #7
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    Re: Simplifying

    dx-bx = ad+bc?
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  8. #8
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    Re: Simplifying

    Thanks alot=)
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  9. #9
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    Re: Simplifying

    You're welcome
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  10. #10
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    Re: Simplifying

    Quote Originally Posted by cristianodoni72 View Post
    (x-a)/b-(x+c)/d=0
    Keep it simple; first, cross multiply:

    d(x - a) = b(x + c) ; expand:

    xd - ad = xb + bc ; get x's together:

    xd - xb = ad + bc ; take out the x:

    x(d - b ) = ad + bc ; finish off:

    x = (ad + bc) / (d - b)
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  11. #11
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    Re: Simplifying

    Quote Originally Posted by procyon View Post
    btw Prove It, How do you get the horizontal line for divide?

    thx

    Pro
    [tex]\dfrac{ax+b}{cx+d}[/tex] is the same as \dfrac{ax+b}{cx+d}
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  12. #12
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    Re: Simplifying

    Hi e^(i*pi),

    \dfrac{Thank}{you}
    That's great, many thanks

    Pro
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