Los 2(x-2y)^-frac{1{2}}(3x+y)^frac{1{3}}-4(x-2y)^-frac{5{2}}(3x+y) op

$$2 ( x - 2 y ) ^ { - \frac { 1 } { 2 } } ( 3 x + y ) ^ { \frac { 1 } { 3 } } - 4 ( x - 2 y ) ^ { - \frac { 5 } { 2 } } ( 3 x + y )$$

Factoriseren

$$\frac{2\sqrt[3]{3x+y}\left(\left(x-2y\right)^{2}-2\left(3x+y\right)^{\frac{2}{3}}\right)}{\left(x-2y\right)^{\frac{5}{2}}}$$

Oplossingsstappen

Factoriseer 2.

$$2\left(\frac{\sqrt[3]{3x+y}}{\sqrt{x-2y}}-\frac{2\left(3x+y\right)}{\left(x-2y\right)^{\frac{5}{2}}}\right)$$

Houd rekening met \left(x-2y\right)^{-\frac{1}{2}}\sqrt[3]{3x+y}-2\left(x-2y\right)^{-\frac{5}{2}}\left(3x+y\right). Factoriseer \frac{\sqrt[3]{3x+y}}{\sqrt{x-2y}}.

$$\frac{\sqrt[3]{3x+y}\left(1-\frac{2\left(3x+y\right)^{\frac{2}{3}}}{\left(x-2y\right)^{2}}\right)}{\sqrt{x-2y}}$$

Herschrijf de volledige gefactoriseerde expressie.

$$\frac{2\sqrt[3]{3x+y}\left(1-\frac{2\left(3x+y\right)^{\frac{2}{3}}}{\left(x-2y\right)^{2}}\right)}{\sqrt{x-2y}}$$

Evalueren

$$\frac{2\sqrt[3]{3x+y}\left(\left(x-2y\right)^{2}-2\left(3x+y\right)^{\frac{2}{3}}\right)}{\left(x-2y\right)^{\frac{5}{2}}}$$