Решебник по алгебре 8 класс Мерзляк ФГОС Задание 158

 

\[\boxed{\text{158\ (158).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\frac{4 - a}{8a^{3}} \cdot \frac{12a^{5}}{a^{2} - 16} =\]

\[= \frac{(4 - a) \cdot 12a^{5}}{8a^{3} \cdot (a - 4)(a + 4)} =\]

\[= \frac{- 3a^{2}}{2 \cdot (a + 4)}\]

\[2)\ \frac{4c - d}{c^{2} + cd} \cdot \frac{2c^{2} - 2d^{2}}{4c^{2} - cd} =\]

\[= \frac{(4c - d)(c - d)(c + d) \cdot 2}{c(c + d) \cdot c \cdot (4c - d)} =\]

\[= \frac{2 \cdot (c - d)}{c^{2}}\]

\[3)\ \frac{b^{2} - 6b + 9}{b^{2} - 3b + 9} \cdot \frac{b^{3} + 27}{5b - 15} =\]

\[= \frac{(b - 3)^{2} \cdot (b + 3) \cdot \left( b^{2} - 3b + 9 \right)}{\left( b^{2} - 3b + 9 \right) \cdot 5 \cdot (b - 3)} =\]

\[= \frac{b^{2} - 9}{5}\]

\[4)\ \frac{a^{3} - 16a}{3a^{2}b} \cdot \frac{12ab^{2}}{4a + 16} =\]

\[= \frac{a(a - 4)(a + 4) \cdot 12ab^{2}}{3a^{2}b \cdot 4 \cdot (a + 4)} =\]

\[= b(a - 4)\]

\[5)\ \frac{a^{3} + b^{3}}{a^{2} - b^{2}} \cdot \frac{7a - 7b}{a^{2} - ab + b^{2}} =\]

\[= \frac{(a + b)\left( a^{2} - ab + b^{2} \right) \cdot 7(a - b)}{(a - b)(a + b)\left( a^{2} - ab + b^{2} \right)} = 7\]

\[6)\ \frac{x^{2} - 9}{x + y} \cdot \frac{5x + 5y}{x^{2} - 3x} =\]

\[= \frac{(x - 3)(x + 3) \cdot 5 \cdot (x + y)}{(x + y) \cdot x \cdot (x - 3)} =\]

\[= \frac{5x + 15}{x}\text{\ \ }\]

\[7)\ \frac{m + 2n}{2 - 3m}\ :\frac{m^{2} + 4mn + 4n^{2}}{3m^{2} - 2m} =\]

\[= \frac{(m + 2n) \cdot m \cdot (3m - 2)}{(2 - 3m)(m + 2n)^{2}} =\]

\[= \frac{- m}{m + 2n}\]

\[8)\ \frac{a^{3} + 8}{16 - a^{4}}\ :\frac{a^{2} - 2a + 4}{a^{2} + 4} =\]

\[= \frac{(a + 2)\left( a^{2} - 2a + 4 \right)\left( a^{2} + 4 \right)}{\left( 4 - a^{2} \right)\left( 4 + a^{2} \right)\left( a^{2} - 2a + 4 \right)} =\]

\[= \frac{a + 2}{4 - a^{2}} =\]

\[= \frac{(a + 2)}{(2 - a)(2 + a)} = \frac{1}{2 - a}\]

\[9)\ \frac{x^{2} - 12x + 36}{3x + 21} \cdot \frac{x^{2} - 49}{4x - 24} =\]

\[= \frac{(x - 6)^{2} \cdot (x - 7)(x + 7)}{3(x + 7) \cdot 4 \cdot (x - 6)} =\]

\[= \frac{(x - 6)(x - 7)}{12}\]

\[10)\ \frac{3a + 15b}{a^{2} - 81b^{2}}\ :\]

\[:\frac{4a + 20b}{a^{2} - 18ab + 81b^{2}} =\]

\[= \frac{3(a + 5b)(a - 9b)^{2}}{(a - 9b)(a + 9b) \cdot 4 \cdot (a + 5b)} =\]

\[= \frac{3 \cdot (a - 9b)}{4 \cdot (a + 9b)}\]

\[\boxed{\text{158.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\frac{a^{2} - 81}{a^{2} - 8a}\ :\frac{a - 9}{a^{2} - 64} =\]

\[= \frac{(a - 9)(a + 9)(a - 8)(a + 8)}{a(a - 8)(a - 9)} =\]

\[= \frac{(a + 9)(a + 8)}{a}\]

\[если\ a = - 4:\ \]

\[\frac{( - 4 + 9)( - 4 + 8)}{- 4} = \frac{5 \cdot 4}{- 4} = - 5.\]

\[2)\ \frac{x}{4x^{2} - 4y^{2}}\ :\frac{1}{6x + 6y} =\]

\[= \frac{x \cdot 6 \cdot (x + y)}{4(x + y)(x - y)} = \frac{3x}{2(x - y)}\]

\[если\ x = 4,2;\ \ y = - 2,8:\ \]

\[\frac{3 \cdot 4,2}{2(4,2 + 2,8)} = \frac{12,6}{14} = 0,9.\ \]

\[3)\ \left( 3a^{2} - 18a + 27 \right)\ :\frac{3a - 9}{4a} =\]

\[= \frac{3(a - 3)^{2} \cdot 4a}{3(a - 3)} = 4a(a - 3)\]

\[если\ a = 0,5:\ \]

\[4 \cdot 0,5 \cdot (0,5 - 3) = 2 \cdot ( - 2,5) =\]

\[= - 5.\]

\[4)\ \frac{a^{6} + a^{5}}{(3a - 3)^{2}}\ :\frac{a^{5} + a^{4}}{9a^{2} - 9a} =\]

\[= \frac{\left( a^{6} + a^{5} \right) \cdot 9a \cdot (a - 1)}{3 \cdot (a - 1)^{2} \cdot \left( a^{5} + a^{4} \right)} =\]

\[= \frac{\left( a^{6} + a^{5} \right) \cdot a}{(a - 1)\left( a^{5} + a^{4} \right)}\]

\[при\ a = 0,8:\]

\[\frac{{((0,8)}^{6} + (0,8)^{5}) \cdot 0,8}{(0,8 - 1){((0,8)}^{5} + (0,8)^{4})} =\]

\[= \frac{(0,8)^{7} + (0,8)^{6}}{- 0,2{((0,8)}^{5} + (0,8)^{4})} =\]

\[= \frac{(0,8)^{6}(0,8 + 1)}{- 0,2(0,8)^{4}(0,8 + 1)} =\]

\[= \frac{(0,8)^{2}}{- 0,2} = - 3,2.\]