Номер 46 гдз 8 класс алгебра Муравин Муравина


Номер 46

 

\begin{equation} 1)\frac{27a^{3}b^{4}-9a^{2}b^{5}}{81a^{4}b^{2}-27a^{3}b^{3}}= \end{equation} \begin{equation} =\frac{9a^{2}b^{4}(3a-b)}{27a^{3}b^{2}(3a-b)}= \end{equation} \begin{equation} =\frac{a^{2}b^{4}}{3a^{3}b^{2}}= \end{equation} \begin{equation} =\frac{a^{2}\cdot b^{2}\cdot b^{2}}{3a^{3}\cdot a\cdot b^{2}}=\frac{b^{2}}{3a}; \end{equation} \begin{equation} 2)\frac{16x^{2}y^{3}-24xy^{4}}{24x^{3}y^{2}-36x^{2}y^{3}}= \end{equation} \begin{equation} =\frac{8y^{3}x(2x-3y)}{6x^{2}y^{2}(4x-6y)}= \end{equation} \begin{equation} =\frac{8y^{3}x\cdot (2x-3y)}{12x^{2}y^{2}\cdot (2x-3y)}= \end{equation} \begin{equation} =\frac{2\cdot y^{2}\cdot y\cdot x}{3x\cdot x\cdot y^{2}}=\frac{2y}{3x}; \end{equation} \begin{equation} 3)\frac{(a-b)^{2}}{b^{2}-a^{2}}= \end{equation} \begin{equation} =\frac{(b-a)^{2}}{(b-a)(b+a)}= \end{equation} \begin{equation} =\frac{b-a}{b+a}; \end{equation} \begin{equation} 4)\frac{2a+6c}{a^{2}-9c^{2}}= \end{equation} \begin{equation} =\frac{2(a+3c)}{(a-3c)(a+3c)}= \end{equation} \begin{equation} =\frac{2}{a+3c}; \end{equation} \begin{equation} 5)\frac{(x-4y)^{2}}{x^{2}-16y^{2}}= \end{equation} \begin{equation} =\frac{(x-4y)^{2}}{(x+4y)(x-4y)}= \end{equation} \begin{equation} =\frac{x-4y}{x+4y}; \end{equation} \begin{equation} 6)\frac{9-6a+a^{2}}{a^{2}-9}= \end{equation} \begin{equation} =\frac{a^{2}-6a+9}{a^{2}-9}= \end{equation} \begin{equation} =\frac{(a-3)^{2}}{a^{2}-9}= \end{equation} \begin{equation} =\frac{(a-3)^{2}}{(a-3)(a+3)}= \end{equation} \begin{equation} =\frac{a-3}{a+3}; \end{equation} \begin{equation} 7)\frac{8c^{3}+12c^{2}d+}{} \end{equation} \begin{equation} \frac{+6cd^{2}+d^{3}}{4c^{2}+4cd+d^{2}}= \end{equation} \begin{equation} =2c+d \end{equation} 8c3 + 12c2d + 6cd2 + d2 =
= (8c3 + d3) + (12c2d + 6cd2) =
= (2c + d)(4c2 - 2cd + d2) + 6cd(2c + d) =
= (2c + d)(4c2 - 2cd + d2 + 6cd) =
= (2c + d)(4c2 + 4cd + d2) =
= (2c + d)(2c + d)2 = (2c + d)3 \begin{equation} \frac{(2c+d)^{3}}{(2c+d)^{2}}=2c+d; \end{equation} \begin{equation} 8)\frac{27d^{3}-27d^{2}b+}{9d^{2}-} \end{equation} \begin{equation} \frac{+9db^{2}-b^{3}}{-6bd+b^{2}}= \end{equation} \begin{equation} =3d-b \end{equation} 9d2 - 6bd + b2 =
= (3d - b)2 (27d3 - b3) - (27d2b - 9db2) =
= (3d - b)(9d2 + 3db + b2) - 9db(3d - b) =
= (3d - b)(9d2 + 3db - 9db) + b2 =
= (3d - b)(9d2 - 6db + b2) =
= (3d - b)(3d - b)2 = (3d - b)3 \begin{equation} \frac{(3d-b)^{3}}{(3d-b)^{2}}=3d-b. \end{equation}

Play
Play
previous arrow
next arrow
Slider