If lim_x 1 0.05em (5x+1 )^1/3- (x+5 )^1/3 (2x+3 )^1/2- (x+4 )^1/2= m 5n (2n )^2/3, where gcd ⁡ (m ,n )=1, then 8m+12n is equal to______

Question

Accepted Answer

Correct answer: 100. (100) lim_x 1 0.05em 13 (5x+1 )^-2/35- 13 (x+5 )^-2/3 12 (2x+3 )^-1/2 2- 12 (x+4 )^-1/2 = 83 56^2/3m=88m+12n=100

$If lim_{x \to 1} \frac{( 5 x + 1 ) ^{1/3} - ( x + 5 ) ^{1/3}}{( 2 x + 3 ) ^{1/2} - ( x + 4 ) ^{1/2}} = \frac{m 5}{n ( 2 n ) ^{2/3}}, where gcd (m, n) = 1, then 8 m + 12 n is equal to______$