Respuestas

2014-01-15T23:31:35+01:00
2.  \frac{8a^{5}b}{27x^{2}b^{3}} :  \frac{32ab^{4}}{81x^{4}b^{6}}   \\  \\  \frac{8a^{5}b}{27x^{2}b^{3}} * \frac{81x^{4}b^{6}}{32ab^{4}}   \\  \\  \frac{8a^{5}b}{32ab^{4}}* \frac{81x^{4}b^{6}}{27x^{2}b^{3}}   \\  \\  \frac{1}{4} a^{(5-1)}b^{(1-4)}*3x^{(4-2)}b^{(6-3)} \\  \\ \frac{1}{4} a^{4} b^{-3}*3x^{2}b^{3} \\  \\  \frac{3}{4}a^{4}b^{(-3+3)}x^{2} \\  \\  \frac{3}{4}a^{4}b^{0}x^{2} \\  \\  \frac{3}{4} a^{4}*1* x^{2}  \\  \\  \frac{3}{4}a^{4} x^{2}


3.  \frac{4t^{2}+t-3}{2t^{2}-t-1}: \frac{2t^{2}+t-1}{1- t^{3}} \\  \\   \frac{4t^{2}+t-3}{2t^{2}-t-1}* \frac{1- t^{3}}{2t^{2}+t-1}   \\  \\  \frac{(t+1)(4t-3)}{(t-1)(2t+1)}* \frac{-(t^{3}-1)}{(t+1)(2t-1)} \\  \\ \frac{(t+1)(4t-3)}{(t-1)(2t+1)}* \frac{-[(t-1)(t^{2}+t+1)[}{(t+1)(2t-1)}  \\  \\  \frac{-(t^{2}+t+1)(4t-3)}{4t^{2}-1}


4.  \frac{x+3y}{x-y}: \frac{ x^{2}-9y^{2}}{x^{2}-y^{2}} \\  \\  \frac{x+3y}{x-y}* \frac{x^{2}-y^{2}}{ x^{2}-9y^{2}} \\  \\   \frac{x+3y}{x-y}* \frac{(x+y)(x-y)}{(x+3y)(x-3y)} \\  \\  \frac{x+y}{x-3y}


5.  \frac{ x^{2}-2x+1}{ x^{2}-1}: \frac{3x-3 x^{2}}{2x+2} \\  \\  \frac{ x^{2}-2x+1}{ x^{2}-1}* \frac{2x+2}{3x-3 x^{2}} \\  \\  \frac{(x-1)(x-1)}{(x+1)(x-1)}* \frac{2(x+1)}{3x(1-x)} \\  \\    \frac{2(x-1)}{3x(1-x)}


6.  \frac{a^{2}+15a+54}{a^{2}+5a-36}: \frac{a^{2}+2a-24}{a^{2}+16-8a} \\  \\  \frac{a^{2}+15a+54}{a^{2}+5a-36}* \frac{a^{2}-8a+16}{a^{2}+2a-24} \\  \\  \frac{(a+9)(a+6)}{(a+9)(a-4)}* \frac{(a-4)(a-4)}{(a+6)(a-4)} \\  \\ =1


7.  \frac{3x^{2}+7xy-6y^{2}}{3x^{2}-19xy+20y^{2}}: \frac{7x^{2}+20xy-3y^{2}}{7x^{2}-36xy+5y^{2}} \\  \\  \frac{3x^{2}+7xy-6y^{2}}{3x^{2}-19xy+20y^{2}}*  \frac{7x^{2}-36xy+5y^{2}}{7x^{2}+20xy-3y^{2}} \\  \\  \frac{(x+3y)(3x-2y)}{(x-5y)(3x-4y)}* \frac{(x-5y)(7x-y)}{(x+3y)(7x-y)} \\  \\  \frac{3x-2y}{3x-4y}


8.  \frac{x^{3}-3x^{2}+3x-1}{ x^{2}-81}: \frac{ x^{2}-2x+1}{ x^{2}-18x+81} \\  \\ \frac{x^{3}-3x^{2}+3x-1}{ x^{2}-81}* \frac{x^{2}-18x+81}{x^{2}-2x+1} \\  \\  \frac{( x^{3}-1)-(3 x^{2}-3x)}{(x+9)(x-9)}* \frac{(x-9)^{2}}{(x-1)(x-1)} \\  \\  \frac{1(x^{3} -1)-3x(x-1)}{(x+9)(x-9)}* \frac{(x-9)^{2}}{(x-1)(x-1)} \\  \\  \frac{(1-3x)( x^{3}-1)(x-1)}{(x+9)(x-9)}* \frac{(x-9)^{2}}{(x-1)(x-1)} \\  \\   \frac{(1-3x)(x-1)(x^{2}+x+1)(x-1)(x-9)^{2}}{(x+9)(x-9)(x-1)(x-1)} \\  \\  \frac{(1-3x)(x^{2}+x+1)(x-9)}{(x+9)}
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Los resolví aplicando factoreo, y usando las herramientas que te proporciona el sistema mismo, utilizando las fórmulas del recuadro que se encuentra en la parte de abajo.
Te dejo el link donde están los casos de factoreo para que practiques: http://www.fic.umich.mx/~lcastro/2%20factorizacion.pdf
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