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when adding or subtracting rational exprssions, why do you need an LCD

  • algebra -

    The rules for numerators and denominators are different. When adding or subtracting fractions, or fractional algebraic terms, the denominators must be the same. Then, you can add or subtract the numerators while keeping the common denominator.

    The reason should be obvious when you think about it. When you have a series of numbers with the same denominator x, the ratio of their sizes is the ratio of the numerators.
    Thus a/x + b/x = (a+b)*(1/x) = (a+b)/x

    You cannot write an analogous valid expression to justify adding denominators with a common numerator. instead, you have
    x/a + x/b = x(1/a + 1/b), = x(b+a)/ab

  • algebra -

    3 4/9 x 1 4/5 show work please

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