Solucionar -mu_{A}m_{A}gcosθ-m_{A}g[frac{m_{A}(sinθ-mu_{A}cosθ)+m_{A}(sinθ-mu_{B}cosθ)}{(m_{A}+m_{A})}]

$$- \mu _ { A } m _ { A } g \cos \theta - m _ { A } g [ \frac { m _ { A } ( \sin \theta - \mu _ { A } \cos \theta ) + m _ { A } ( \sin \theta - \mu _ { B } \cos \theta ) } { ( m _ { A } + m _ { A } ) } ]$$

Factorizar

$$\frac{gm_{A}\left(\mu _{B}\cos(\theta )-\mu _{A}\cos(\theta )-2\sin(\theta )\right)}{2}$$

Pasos de la solución

Combina m_{A} y m_{A} para obtener 2m_{A}.

$$factor(\left(-\mu _{A}\right)m_{A}g\cos(\theta )-m_{A}g\times \frac{m_{A}\left(\sin(\theta )-\mu _{A}\cos(\theta )\right)+m_{A}\left(\sin(\theta )-\mu _{B}\cos(\theta )\right)}{2m_{A}})$$

Factorice las expresiones que aún no se hayan factorizado en \frac{m_{A}\left(\sin(\theta )-\mu _{A}\cos(\theta )\right)+m_{A}\left(\sin(\theta )-\mu _{B}\cos(\theta )\right)}{2m_{A}}.

$$factor(\left(-\mu _{A}\right)m_{A}g\cos(\theta )-m_{A}g\times \frac{m_{A}\left(-\mu _{A}\cos(\theta )-\mu _{B}\cos(\theta )+\sin(\theta )+\sin(\theta )\right)}{2m_{A}})$$

Anula m_{A} tanto en el numerador como en el denominador.

$$factor(\left(-\mu _{A}\right)m_{A}g\cos(\theta )-m_{A}g\times \frac{-\mu _{A}\cos(\theta )-\mu _{B}\cos(\theta )+\sin(\theta )+\sin(\theta )}{2})$$

Combina \sin(\theta ) y \sin(\theta ) para obtener 2\sin(\theta ).

$$factor(\left(-\mu _{A}\right)m_{A}g\cos(\theta )-m_{A}g\times \frac{-\mu _{A}\cos(\theta )-\mu _{B}\cos(\theta )+2\sin(\theta )}{2})$$

Expresa m_{A}\times \frac{-\mu _{A}\cos(\theta )-\mu _{B}\cos(\theta )+2\sin(\theta )}{2} como una única fracción.

$$factor(\left(-\mu _{A}\right)m_{A}g\cos(\theta )-\frac{m_{A}\left(-\mu _{A}\cos(\theta )-\mu _{B}\cos(\theta )+2\sin(\theta )\right)}{2}g)$$

Usa la propiedad distributiva para multiplicar m_{A} por -\mu _{A}\cos(\theta )-\mu _{B}\cos(\theta )+2\sin(\theta ).

$$factor(\left(-\mu _{A}\right)m_{A}g\cos(\theta )-\frac{-m_{A}\mu _{A}\cos(\theta )-m_{A}\mu _{B}\cos(\theta )+2m_{A}\sin(\theta )}{2}g)$$

Expresa \frac{-m_{A}\mu _{A}\cos(\theta )-m_{A}\mu _{B}\cos(\theta )+2m_{A}\sin(\theta )}{2}g como una única fracción.

$$factor(\left(-\mu _{A}\right)m_{A}g\cos(\theta )-\frac{\left(-m_{A}\mu _{A}\cos(\theta )-m_{A}\mu _{B}\cos(\theta )+2m_{A}\sin(\theta )\right)g}{2})$$

Usa la propiedad distributiva para multiplicar -m_{A}\mu _{A}\cos(\theta )-m_{A}\mu _{B}\cos(\theta )+2m_{A}\sin(\theta ) por g.

$$factor(\left(-\mu _{A}\right)m_{A}g\cos(\theta )-\frac{-m_{A}\mu _{A}\cos(\theta )g-m_{A}\mu _{B}\cos(\theta )g+2m_{A}\sin(\theta )g}{2})$$

Simplifica \frac{1}{2}.

$$\frac{m_{A}g\left(-2\mu _{A}\cos(\theta )-\left(-\mu _{A}\cos(\theta )-\mu _{B}\cos(\theta )+2\sin(\theta )\right)\right)}{2}$$

Calcular

$$\frac{gm_{A}\left(\mu _{B}\cos(\theta )-\mu _{A}\cos(\theta )-2\sin(\theta )\right)}{2}$$