Калькуляторы онлайн/ Решение уравнений/ Упрощение выражений/ Сократить дробь/ (k/(p*(t1*p+1)))*((t2*p+1)/(t3*p+1))*(p/(t4*p+1))

Сократим дробь (k/(p*(t1*p+1)))*((t2*p+1)/(t3*p+1))*(p/(t4*p+1))

Учитель очень удивится увидев твоё верное решение 😼

Примеры

Решение

Вы ввели [src]
     k       t2*p + 1    p    
------------*--------*--------
p*(t1*p + 1) t3*p + 1 t4*p + 1
$$\frac{p}{p t_{4} + 1} \frac{k}{p \left(p t_{1} + 1\right)} \frac{p t_{2} + 1}{p t_{3} + 1}$$
Степени [src]
          k*(1 + p*t2)          
--------------------------------
(1 + p*t1)*(1 + p*t3)*(1 + p*t4)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
Численный ответ [src]
k*(1.0 + p*t2)/((1.0 + p*t1)*(1.0 + p*t3)*(1.0 + p*t4))
Рациональный знаменатель [src]
          k*(1 + p*t2)          
--------------------------------
(1 + p*t1)*(1 + p*t3)*(1 + p*t4)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
Объединение рациональных выражений [src]
          k*(1 + p*t2)          
--------------------------------
(1 + p*t1)*(1 + p*t3)*(1 + p*t4)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
Общее упрощение [src]
          k*(1 + p*t2)          
--------------------------------
(1 + p*t1)*(1 + p*t3)*(1 + p*t4)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
Собрать выражение [src]
          k*(1 + p*t2)          
--------------------------------
(1 + t1*p)*(1 + t3*p)*(1 + t4*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + t2*p)          
--------------------------------
(1 + p*t3)*(1 + p*t4)*(1 + t1*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + t2*p)          
--------------------------------
(1 + t1*p)*(1 + t3*p)*(1 + t4*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + t2*p)          
--------------------------------
(1 + p*t4)*(1 + t1*p)*(1 + t3*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + t2*p)          
--------------------------------
(1 + p*t1)*(1 + t3*p)*(1 + t4*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + p*t2)          
--------------------------------
(1 + p*t1)*(1 + p*t3)*(1 + t4*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + t2*p)          
--------------------------------
(1 + p*t3)*(1 + t1*p)*(1 + t4*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + p*t2)          
--------------------------------
(1 + p*t4)*(1 + t1*p)*(1 + t3*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + p*t2)          
--------------------------------
(1 + p*t3)*(1 + t1*p)*(1 + t4*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + t2*p)          
--------------------------------
(1 + p*t1)*(1 + p*t3)*(1 + p*t4)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + p*t2)          
--------------------------------
(1 + p*t3)*(1 + p*t4)*(1 + t1*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + p*t2)          
--------------------------------
(1 + p*t1)*(1 + p*t3)*(1 + p*t4)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + p*t2)          
--------------------------------
(1 + p*t1)*(1 + t3*p)*(1 + t4*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + t2*p)          
--------------------------------
(1 + p*t1)*(1 + p*t3)*(1 + t4*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + t2*p)          
--------------------------------
(1 + p*t1)*(1 + p*t4)*(1 + t3*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
          k*(1 + p*t2)          
--------------------------------
(1 + p*t1)*(1 + p*t4)*(1 + t3*p)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
Комбинаторика [src]
          k*(1 + p*t2)          
--------------------------------
(1 + p*t1)*(1 + p*t3)*(1 + p*t4)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$
Общий знаменатель [src]
                              k + k*p*t2                             
---------------------------------------------------------------------
                                2          2          2             3
1 + p*t1 + p*t3 + p*t4 + t1*t3*p  + t1*t4*p  + t3*t4*p  + t1*t3*t4*p
$$\frac{k p t_{2} + k}{p^{3} t_{1} t_{3} t_{4} + p^{2} t_{1} t_{3} + p^{2} t_{1} t_{4} + p^{2} t_{3} t_{4} + p t_{1} + p t_{3} + p t_{4} + 1}$$
Раскрыть выражение [src]
          k*(t2*p + 1)          
--------------------------------
(t1*p + 1)*(t3*p + 1)*(t4*p + 1)
$$\frac{k \left(p t_{2} + 1\right)}{\left(p t_{1} + 1\right) \left(p t_{3} + 1\right) \left(p t_{4} + 1\right)}$$