12. Выполнить действия: 1) (3x+5)/(x−2) − (11−x)/(x−2); 2) 2a/(a−b) + (2a−b)/(b−a); 3) 3/a + 5 − 2/(a−b); 4) 3a/(6a+8) − 1/2 − 2/(4−3a); 5) (5b−b²)/(3a) · 6a²/(b³−5b²); 6) 6c³/(9−a²) · (a³−6a+9)/(4a²c); 7) a³b/(3a−6b) : (a²b²−a²b)/(ac−2bc); 8) (10−15b)/(a−b)² : (9b²−4)/(3b−3a); 9) (a/(7a−4) − 1/(a+3)) · (12−21a)/(2−a)²; 10) (x/(x−2) − x/(x+2) − (x²+4)/(4−x²)) : (2x+x²)/(2−x)².

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Accepted Answer

\(\frac{3x+5}{x-2}-\frac{11-x}{x-2}=\frac{4x-6}{x-2}=\frac{2(2x-3)}{x-2}\).
\(\frac{2a}{a-b}+\frac{2a-b}{b-a}=\frac{b}{a-b}\).
\(\frac3a+5-\frac2{a-b}=\frac{5a^2-5ab+a-3b}{a(a-b)}\).
\(\frac{3a}{6a+8}-\frac12-\frac2{4-3a}=\frac{16}{9a^2-16}\).
\(\frac{5b-b^2}{3a}\cdot\frac{6a^2}{b^3-5b^2}=-\frac{2a}{b}\).
\(\frac{6c^3}{9-a^2}\cdot\frac{a^3-6a+9}{4a^2c}=\frac{3c^2(a^3-6a+9)}{2a(9-a^2)}\).
\(\frac{a^3b}{3a-6b}:\frac{a^2b^2-a^2b}{ac-2bc}=\frac{ac(a-2)}{3(a-2b)(b-1)}\).
\(\frac{10-15b}{(a-b)^2}:\frac{9b^2-4}{3b-3a}=\frac{15(3b-2)}{(a-b)(3b+2)}\).
\(\left(\frac{a}{7a-4}-\frac1{a+3}\right)\cdot\frac{12-21a}{(2-a)^2}=-\frac3{a+3}\).
\(\left(\frac{x}{x-2}-\frac{x}{x+2}-\frac{x^2+4}{4-x^2}\right):\frac{2x+x^2}{(2-x)^2}=\frac{x-2}{x}\).

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