Simplify (4x(x+6)^4-x^2*8(x+6)^3)/((x+6)^8)

Problem

(4*x*(x+6)4−x2⋅8*(x+6)3)/((x+6)8)

Solution

1. Identify the common factors in the numerator. Both terms in the numerator contain 4*x and (x+6)3

2. Factor out the greatest common factor 4*x*(x+6)3 from the numerator.

(4*x*(x+6)3*[(x+6)−2*x])/((x+6)8)

3. Simplify the expression inside the brackets by combining like terms.

(4*x*(x+6)3*(6−x))/((x+6)8)

4. Reduce the fraction by dividing both the numerator and the denominator by (x+6)3

(4*x*(6−x))/((x+6)5)

5. Distribute the 4*x in the numerator to reach the final simplified form.

(24*x−4*x2)/((x+6)5)

Final Answer

(4*x*(x+6)4−x2⋅8*(x+6)3)/((x+6)8)=(24*x−4*x2)/((x+6)5)

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