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Precalc

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There's f(x) = (2x+3)/(x+4)
and g(x) = (4x-3)/(2-x)

Solve for x in f(g(x))

I tried this but I could not end up with the answer being x

  • Precalc -

    f(g(x) = [2(4x-3)/(2-x) + 3]/[(4x-3)/(2-x) + 4]

    = [(8x-6 + 6-3x)/(2-x)] / [(4x-3 + 8-4x)/(2-x)]

    = [5x/(2-x)] / [5/(2-x)]
    = [5x/(2-x)] [(2-x)/5]
    = 5x/5
    = x

  • Precalc -

    thank you so much

  • Precalc -

    welcome

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