4/(3(x+4)^3) *[1/(x+2)^2 - (x+2)/(x+4)^4]43(x+4)3⋅[1(x+2)2−x+2(x+4)4]
Given:
(((x+4)^3)/4 * (x+2)^-2/3 - (x+2)/3 * (x+4)^-1/4)/((x+4)^3/4)^2(x+4)34⋅(x+2)−23−x+23⋅(x+4)−14((x+4)34)2
Let a = x+4a=x+4 and b=x+2b=x+2
((a^3)/4 * b^-2/3 - b/3 * a^-1/4)/(a^3/4)^2a34⋅b−23−b3⋅a−14(a34)2
When you divide by a fraction, you are multiplying the reciprocal:
[(a^3)/4 * b^-2/3 - b/3 * a^-1/4] * (4/a^3)^2[a34⋅b−23−b3⋅a−14]⋅(4a3)2
Change negative exponents to reciprocals with positive exponents:
[(a^3)/4 * 1/(3b^2) - b/3 * 1/(4a)] * (4/a^3)^2[a34⋅13b2−b3⋅14a]⋅(4a3)2
[a^3/(12b^2) - b/(12a)] (16/a^6)[a312b2−b12a](16a6)
(16a^3)/(12a^6b^2) - (16b)/(12a^7)16a312a6b2−16b12a7
4/(3a^3b^2) - (4b)/(3a^7)43a3b2−4b3a7
Factor out 4/(3a^3)43a3:
4/(3a^3) [1/b^2 - b/a^4]43a3[1b2−ba4]
Substitute back in x+4x+4 and x+2x+2
4/(3(x+4)^3) * [1/(x+2)^2 - (x+2)/(x+4)^4]43(x+4)3⋅[1(x+2)2−x+2(x+4)4]
Hope that was helpful.
