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Math Help - Comparing equations with denominators

  1. #1
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    Comparing equations with denominators

    equation is

    a +b x / c+d x = 3 +4 x / 5+6 x where a,b,c,d are constants

    So by comparing can we say that

    a=3,b=4,c=5,d=6?
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  2. #2
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    Re: Comparing equations with denominators

    I am not sure as to what are you trying to do. I can also say that by having a = 6, b= 8, c =10 and d = 12 the equation is still satisfied. so pl tell us what exactly do you want to do or find out.
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  3. #3
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    Re: Comparing equations with denominators

    if this equation is always true are those the only solutions?
    if yes is there any proof of that?
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  4. #4
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    Re: Comparing equations with denominators

    Quote Originally Posted by AaPa View Post
    equation is

    a +b x / c+d x = 3 +4 x / 5+6 x where a,b,c,d are constants

    So by comparing can we say that

    a=3,b=4,c=5,d=6?
    yes
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  5. #5
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    Re: Comparing equations with denominators

    Quote Originally Posted by AaPa View Post
    if this equation is always true are those the only solutions?
    if yes is there any proof of that?
    They are not the only solutions. See ibdutt's post for a second solution. The complete solution set is a = 3n, b = 4n, c = 5n, and d = 6n where n is any (non-zero) real number.=:
    \frac{(3n) + (4n)x}{(5n) + (6n)x} = \frac{n(3 + 4x)}{n(5 + 6x)} = \frac{3 + 4x}{5 + 6x}

    -Dan

    Edit: Also, please use parenthesis when necessary. What you wrote was
    \text{a +b x / c+d x} = a + \frac{bx}{c} + dx
    which is not what you wanted to say. You needed to write this as
    (a + b x)/(c + d x)
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  6. #6
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    Re: Comparing equations with denominators

    thanks
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