Question

Ayuda pls Matemática ​

Answer 1

2.

a)

$\dfrac{ax^3-x^2}{x^2y}=\dfrac{x^2(ax-1)}{x^2y}=\boxed{\dfrac{ax-1}{y}}$

b)

$\dfrac{x^2+xy+x+y}{x^2-1}=\dfrac{x(x+y)+(x+y)}{(x+1)(x-1)}=\dfrac{(x+1)(x+y)}{(x+1)(x-1)}=\boxed{\dfrac{x+y}{x-1}}$

c)

$\dfrac{x^2-144}{x-12}=\dfrac{(x+12)(x-12)}{(x-12)}=\boxed{x+12}$

d)

$\dfrac{a^2-14a+49}{3a-21}=\dfrac{(a-7)^2}{3(a-7)}=\boxed{\dfrac{a-7}{3}}$

3.

$\sqrt[4]{23-\sqrt{43+\sqrt{41-\sqrt[3]{125}}}}=\sqrt[4]{23-\sqrt{43+\sqrt{41-5}}}$

$=\sqrt[4]{23-\sqrt{43+\sqrt{36}}}=\sqrt[4]{23-\sqrt{43+6}}=\sqrt[4]{23-\sqrt{49}}$

$=\sqrt[4]{23-7}}=\sqrt[4]{16}=\boxed{2}$