Question

Даю баллл Помогите пожалуйста Срочно нужно .
896. Сократите выражение и найдите его значение.
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Answer 1

Ответ:

$a)\ \ b=-2\dfrac{1}{6}\ \ ,\ \ \dfrac{3b+2}{3b-2}:\Big(\dfrac{18b}{27b^3-8}+\dfrac{6b}{9b^2+6b+4}-\dfrac{1}{3b-2}\Big)-\dfrac{6b+8}{3b-2}=\\\\\\=\dfrac{3b+2}{3b-2}:\Big(\dfrac{18b}{(3b-2)(9b^2+6b+4)}+\dfrac{6b}{9b^2+6b+4}-\dfrac{1}{3b-2}\Big)-\dfrac{6b+8}{3b-2}=\\\\\\=\dfrac{3b+2}{3b-2}:\dfrac{18b+6b(3b-2)-(9b^2+6b+4)}{(3b-2)(9b^2+6b+4)}-\dfrac{6b+8}{3b-2}=\\\\\\=\dfrac{3b+2}{3b-2}:\dfrac{18b+18b^2-12b-9b^2-6b-4}{(3b-2)(9b^2+6b+4)}-\dfrac{6b+8}{3b-2}=$

$=\dfrac{3b+2}{3b-2}\cdot \dfrac{(3b-2)(9b^2+6b+4)}{9b^2-4}-\dfrac{6b+8}{3b-2}=\\\\\\==\dfrac{3b+2}{3b-2}\cdot \dfrac{(3b-2)(9b^2+6b+4)}{(3b-2)(3b+2)}-\dfrac{6b+8}{3b-2}=\dfrac{9b^2+6b+4}{3b-2}-\dfrac{6b+8}{3b-2}=\\\\\\=\dfrac{9b^2+6b+4-6b-8}{3b-2}=\dfrac{9b^2-4}{3b-2}=\dfrac{(3b-2)(3b+2)}{3b-2}=3b+2=\\\\\\=3\cdot (-2\dfrac{1}{6})+2=-3\cdot \dfrac{13}{6}+2=-\dfrac{13}{2}+2=-\dfrac{9}{2}=-4,5$

$b)\ \ a=3^{-1}=\dfrac{1}{3}\ ,\ b=7^{-1}=\dfrac{1}{7}\\\\\\\dfrac{a^2-b^2}{a-b}-\dfrac{a^3-b^3}{a^2-b^2}=\dfrac{(a-b)(a+b)}{a-b}-\dfrac{(a-b)(a^2+ab+b^2)}{(a-b)(a+b)}=\\\\\\=(a+b)-\dfrac{a^2+ab+b^2}{a+b}=\dfrac{(a+b)^2-(a^2+ab+b^2)}{a+b}=\\\\\\=\dfrac{a^2+2ab+b^2-a^2-ab-b^2}{a+b} =\dfrac{ab}{a+b}=\dfrac{\frac{1}{3}\cdot \frac{1}{7}}{\frac{1}{3}+\frac{1}{7}}=\dfrac{\frac{1}{21}}{\frac{7+3}{21}}=\dfrac{1}{7+3}=\dfrac{1}{10}=0,1$