Question

AYUDAAAAA PARA HOY .....URGENTEEEEE! CON RESOLUCION

Answer 1

EJERCICIO 1:

$\:\left(\frac{a^4-27a}{a^2+7a-30}\right)\left(\frac{a^2+20a+100}{a^3+3a^2+9a}\right)\div \frac{a^2-100}{a-3}\\\\=\frac{a^4-27a}{a^2+7a-30}\cdot \frac{\frac{a^2+20a+100}{a^3+3a^2+9a}}{\frac{a^2-100}{a-3}}\\\\=\frac{a\left(a^2+3a+9\right)}{a+10}\cdot \frac{\frac{a^2+20a+100}{a^3+3a^2+9a}}{\frac{a^2-100}{a-3}}\\\\=\frac{a\left(a^2+3a+9\right)\left(a-3\right)\left(a+10\right)}{\left(a+10\right)a\left(a-10\right)\left(a^2+3a+9\right)}$

$=\frac{\left(a^2+3a+9\right)\left(a-3\right)\left(a+10\right)}{\left(a+10\right)\left(a-10\right)\left(a^2+3a+9\right)}\\\\=\frac{\left(a-3\right)\left(a+10\right)}{\left(a+10\right)\left(a-10\right)}\\\\=\frac{a-3}{a-10}$

EJERCICIO 2:

$\left(\frac{\left(a+1\right)^2\left(a^2-a+1\right)^2}{\left(a^3+1\right)^2}\right)\left(\frac{\left(a-1\right)^2\left(a^2+a+1\right)^2}{\left(a^3-1\right)^2}\right)^2\\\\\\=\frac{\left(a+1\right)^2\left(a^2-a+1\right)^2}{\left(a^3+1\right)^2}\left(\frac{\left(a-1\right)^2\left(a^2+a+1\right)^2}{\left(a^3-1\right)^2}\right)\\\\\\=1\cdot \left(\frac{\left(a-1\right)^2\left(a^2+a+1\right)^2}{\left(a^3-1\right)^2}\right)^2\\\\=1\cdot \:1\\\\=1$

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