9b²-a²...

bagnuk02p124ir @bagnuk02p124ir

July 2022 1 5 Report

Спростіть вираз (( a-3b/a²+3ab - a+3b/a²-3ab)) : 4b/9b²-a²

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$1)\dfrac{a-3b}{a^{2}+3ab }-\dfrac{a+3b}{a^{2} -3ab} =\dfrac{a-3b}{a(a+3b)}-\dfrac{a+3b}{a(a-3b)}=\dfrac{(a-3b)\cdot(a-3b)-(a+3b)\cdt(a+3b)}{a(a-3b)(a+3b)}=\\\\=\dfrac{a^{2}-6ab+9b^{2}-a^{2}-6ab-9b^{2}}{a(a-3b)(a+3b)}=-\dfrac{12ab}{a(a-3b)(a+3b)}=\dfrac{12b}{(3b-a)(3b+a)}=\\\\=\dfrac{12b}{9b^{2}-a^{2}}\\\\\\2)\dfrac{12b}{9b^{2}-a^{2}}:\dfrac{4b}{9b^{2}-a^{2}}=\dfrac{12b}{9b^{2} -a^{2} }\cdot\dfrac{9b^{2}-a^{2}}{4b}=\boxed3$

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