Let f, g, and h be three functions defined as : f(x)=5x^2 - 6x - 8, g(x) = 3x^2 - 13x - 10 and  h(x) = 5x + 4/(x-5). If possible, simplify (f/(g*h))(x)

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The functions given are: f(x)=5x^2 - 6x - 8, g(x) = 3x^2 - 13x - 10 and  h(x) = 5x + 4/(x-5)

f(x) = 5x^2 - 6x - 8 = (x - 2)(5x + 4)

g(x) = (x - 5)(3x + 2)

h(x) = (5x(x - 5) + 4)/(x - 5)

(f/(g*h))(x)

=> f(x)/(g(x)*h(x))

=> (x - 2)(5x + 4)(x - 5)/(x - 5)(3x + 2)(5x(x - 5) + 4)

=> (x - 2)(5x + 4)/(3x + 2)(5x(x - 5) + 4)

=> (5x^2 - 10x + 4x - 8)/(15x^3 - 65x^2 - 38x + 8)

The result for (f/(g*h))(x) is (5x^2 - 6x - 8)/(15x^3 - 65x^2 - 38x + 8)

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