Question

упростите выражение (a-b/a - a+b/b) : (1/a2 + 1/b2) при √7-2, b =-2+√7

Answer 1

$(\frac{a-b}{a}-\frac{a+b}{b}):(\frac{1}{a^2}+\frac{1}{b^2})=\\ \\=(\frac{b(a-b)}{ab}-\frac{a(a+b)}{ab}):(\frac{1*b^2}{a^2b^2}+\frac{1*a^2}{a^2b^2})=\\ \\=\frac{b(a-b)-a(a+b)}{ab}:\frac{b^2+a^2}{a^2b^2}=\\ \\=\frac{ab-b^2-a^2-ab}{ab}*\frac{a^2b^2}{b^2+a^2}=\\ \\=\frac{(-b^2-a^2)*a^2b^2}{ab(b^2+a^2)}=\frac{-(b^2+a^2)*ab}{b^2+a^2}=-ab$

$a=\sqrt{7} -2\\b=-2+\sqrt{7}\\ \\-ab=-(\sqrt{7} -2)*(-2+\sqrt{7} )=-(\sqrt{7} -2)(\sqrt{7} -2)=\\ \\=-(\sqrt{7} -2)^2=-((\sqrt{7} )^2-2*2*\sqrt{7} +2^2)=-(7-4\sqrt{7}+4)=-(-4\sqrt{7}+11)=4\sqrt{7}-11$