Question

Помогите решить номер 6.7 по буквами в)г) по действиям

Answer 1

в)
$.............=( frac{st}{(s-t)(s+t)}+ frac{t}{2(t-s)})* frac{s+t}{2t}=( frac{st}{(s-t)(s+t)}-frac{t}{2(s-t)})*frac{s+t}{2t}= \ \ frac{2st-t(s+t)}{2(s-t)(s+t)} *frac{s+t}{2t}= frac{2st-st-t^{2} }{4t(s-t)} = frac{st-t^{2} }{4t(s-t)} = frac{t(s-t)}{4t(s-t)} = frac{1}{4} =0.25$

г)
$..............= frac{3a+b}{ab(a-b)}- frac{a-b}{ab} * frac{3a-b}{(a-b)(a+b)}=frac{3a+b}{ab(a-b)}- frac{3a-b}{ab(a+b)}= \ \ frac{(3a+b)(a+b) - (3a-b)(a-b)}{ab(a+b)(a-b)} = frac{3a^{2}+4ab+b^{2} -3a^{2} +4ab- b^{2} }{ab(a+b)(a-b)} = \ \ frac{8ab}{ab(a+b)(a-b)} = frac{8}{ a^{2} - b^{2} }$