What is lcm x,f(x)=,(f(x)\circ g(x))5-x^3 ?

The solution to lcm x,f(x)=,(f(x)\circ g(x))5-x^3 is (5\circ f(x)g(x)-x^3)f(x)=x

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lcm x,f(x)=,(f(x)\circ g(x))5-x^3

lcm

x, f (x) =, (f (x) \circ g (x)) 5 - x^{3}

(5 \circ f (x) g (x) - x^{3}) f (x) = x

Solution steps

Find Least Common Multiplier of

x, f (x) =, (f (x) \circ g (x)) 5 - x^{3}

Factor

(f (x) \circ g (x)) \cdot 5 - x^{3} : 5 \circ f (x) g (x) - x^{3}

Multiply each factor with the highest power:

(5 \circ f (x) g (x) - x^{3}) \cdot (f (x)) \cdot x

(x^{2} + 3 x)^{2} = 4 (x^{2} + 3 x)

(x - 1) (x + 1) (x + 2) = - 2

x^{2} (x - 2)^{2} (x - 1)^{2} = 0

x^{3} = 9000

2 = y^{3}

What is lcm x,f(x)=,(f(x)\circ g(x))5-x^3 ?
The solution to lcm x,f(x)=,(f(x)\circ g(x))5-x^3 is (5\circ f(x)g(x)-x^3)f(x)=x