simplificar (3u^4v^4-2u^5v^2+(u^2v^2)^2)/(u^3v^2)

Solução

simplificar

\frac{3 u ^{4} v ^{4} - 2 u ^{5} v ^{2} + ( u ^{2} v ^{2} ) ^{2}}{u ^{3} v ^{2}}

2 u (2 v^{2} - u)

Passos da solução

\frac{3 u ^{4} v ^{4} - 2 u ^{5} v ^{2} + ( u ^{2} v ^{2} ) ^{2}}{u ^{3} v ^{2}}

Simplificar

3 u^{4} v^{4} - 2 u^{5} v^{2} + (u^{2} v^{2})^{2} : 4 u^{4} v^{4} - 2 u^{5} v^{2}

= \frac{4 u ^{4} v ^{4} - 2 u ^{5} v ^{2}}{u ^{3} v ^{2}}

Fatorar

4 u^{4} v^{4} - 2 u^{5} v^{2} : 2 u^{4} v^{2} (2 v^{2} - u)

= \frac{2 u ^{4} v ^{2} ( 2 v ^{2} - u )}{u ^{3} v ^{2}}

Eliminar o fator comum:

v^{2}

= \frac{2 u ^{4} ( 2 v ^{2} - u )}{u ^{3}}

Aplicar as propriedades dos expoentes:

a^{b + c} = a^{b} \cdot a^{c}

u^{4} = u^{3} u

= \frac{2 u ^{3} u ( 2 v ^{2} - u )}{u ^{3}}

Eliminar o fator comum:

u^{3}

= 2 u (2 v^{2} - u)

s im pl i f y \frac{x ^{2} - x - 2}{x + 1}

s im pl i f y \frac{9 ^{5}}{9 ^{3}}

s im pl i f y \frac{96}{100}

s im pl i f y - 4^{6}

s im pl i f y 3 (- \frac{3}{2})