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¿Cómo vas a descomponer esta |a|+(|b|-|a|)/(b-a)*(x-a) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src]
      |b| - |a|        
|a| + ---------*(x - a)
        b - a          
$$\frac{- \left|{a}\right| + \left|{b}\right|}{- a + b} \left(- a + x\right) + \left|{a}\right|$$
|a| + ((|b| - |a|)/(b - a))*(x - a)
Simplificación general [src]
(a - b)*|a| - (a - x)*(-|b| + |a|)
----------------------------------
              a - b               
$$\frac{\left(a - b\right) \left|{a}\right| - \left(a - x\right) \left(\left|{a}\right| - \left|{b}\right|\right)}{a - b}$$
((a - b)*|a| - (a - x)*(-|b| + |a|))/(a - b)
Compilar la expresión [src]
(x - a)*(-|a| + |b|)      
-------------------- + |a|
       b - a              
$$\left|{a}\right| + \frac{\left(- a + x\right) \left(- \left|{a}\right| + \left|{b}\right|\right)}{- a + b}$$
(x - a)*(-|a| + |b|)/(b - a) + |a|
Potencias [src]
(x - a)*(-|a| + |b|)      
-------------------- + |a|
       b - a              
$$\left|{a}\right| + \frac{\left(- a + x\right) \left(- \left|{a}\right| + \left|{b}\right|\right)}{- a + b}$$
(x - a)*(-|a| + |b|)/(b - a) + |a|
Denominador racional [src]
(b - a)*|a| + (x - a)*(-|a| + |b|)
----------------------------------
              b - a               
$$\frac{\left(- a + b\right) \left|{a}\right| + \left(- a + x\right) \left(- \left|{a}\right| + \left|{b}\right|\right)}{- a + b}$$
((b - a)*|a| + (x - a)*(-|a| + |b|))/(b - a)
Respuesta numérica [src]
(x - a)*(-|a| + |b|)/(b - a) + |a|
(x - a)*(-|a| + |b|)/(b - a) + |a|
Denominador común [src]
b*|b| + x*|a| - b*|a| - x*|b|      
----------------------------- + |b|
            a - b                  
$$\left|{b}\right| + \frac{- b \left|{a}\right| + b \left|{b}\right| + x \left|{a}\right| - x \left|{b}\right|}{a - b}$$
(b*|b| + x*|a| - b*|a| - x*|b|)/(a - b) + |b|
Combinatoria [src]
a*|b| + x*|a| - b*|a| - x*|b|
-----------------------------
            a - b            
$$\frac{a \left|{b}\right| - b \left|{a}\right| + x \left|{a}\right| - x \left|{b}\right|}{a - b}$$
(a*|b| + x*|a| - b*|a| - x*|b|)/(a - b)
Unión de expresiones racionales [src]
(b - a)*|a| + (x - a)*(-|a| + |b|)
----------------------------------
              b - a               
$$\frac{\left(- a + b\right) \left|{a}\right| + \left(- a + x\right) \left(- \left|{a}\right| + \left|{b}\right|\right)}{- a + b}$$
((b - a)*|a| + (x - a)*(-|a| + |b|))/(b - a)
Parte trigonométrica [src]
(x - a)*(-|a| + |b|)      
-------------------- + |a|
       b - a              
$$\left|{a}\right| + \frac{\left(- a + x\right) \left(- \left|{a}\right| + \left|{b}\right|\right)}{- a + b}$$
(x - a)*(-|a| + |b|)/(b - a) + |a|