Question

7/2*sqrt(11) -4/3*sqrt(7) -5/6*sqrt(11) -9/4*sqrt(7)+sqrt(7)

Answer 1

Respuesta:

$\mathbf{\frac{8\sqrt{11}}{3}-\frac{35\sqrt{7}}{6}}$

Explicación paso a paso:

$\frac{7\sqrt{11}}{2}-\frac{4\sqrt{7}}{3}-\frac{5\sqrt{11}}{6}+(-\frac{9}{4})(\sqrt{7}+\sqrt{7})$

Obtenemos el m.c.m de 2,3,6,4=12

$\frac{42\sqrt{11}-16\sqrt{7}-10\sqrt{11}-27(2\sqrt{7})}{12}$

Realizamos las operaciones correspondientes:

$\frac{42\sqrt{11}-16\sqrt{7}-10\sqrt{11}-54\sqrt{7}}{12}$

Agrupamos los términos semejantes:

$\frac{42\sqrt{11}-10\sqrt{11}-16\sqrt{7}-54\sqrt{7}}{12}$

Simplificamos:

$\frac{32\sqrt{11}-70\sqrt{7}}{12}=\frac{2(16\sqrt{11}-35\sqrt{7})}{12}=\\\\=\frac{2}{12}(16\sqrt{11}-35\sqrt{7})=\frac{1}{6}(16\sqrt{11}-35\sqrt{7})=\\\\=\frac{16\sqrt{11}}{6}-\frac{35\sqrt{7}}{6}=\frac{8\sqrt{11}}{3}-\frac{35\sqrt{7}}{6}$

Saludos