Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
log(3^(x+1)+9)/(9*log(3))-3^((-x)-1)/log(3)-(x+1)/9
¿Cómo vas a descomponer esta log(3^(x+1)+9)/(9*log(3))-3^((-x)-1)/log(3)-(x+1)/9 expresión en fracciones?
Solución
Ha introducido
[src]
/ x + 1 \ -x - 1
log\3 + 9/ 3 x + 1
--------------- - ------- - -----
9*log(3) log(3) 9
$$- \frac{x + 1}{9} + \left(- \frac{3^{- x - 1}}{\log{\left(3 \right)}} + \frac{\log{\left(3^{x + 1} + 9 \right)}}{9 \log{\left(3 \right)}}\right)$$
log(3^(x + 1) + 9)/((9*log(3))) - 3^(-x - 1)/log(3) - (x + 1)/9
Simplificación general
[src]
-x / x\
- 3*3 - (1 + x)*log(3) + log\9 + 3*3 /
----------------------------------------
9*log(3)
$$\frac{- \left(x + 1\right) \log{\left(3 \right)} + \log{\left(3 \cdot 3^{x} + 9 \right)} - 3 \cdot 3^{- x}}{9 \log{\left(3 \right)}}$$
(-3*3^(-x) - (1 + x)*log(3) + log(9 + 3*3^x))/(9*log(3))
Respuesta numérica
[src]
-0.111111111111111 + 0.101137691847426*log(3^(x + 1) + 9) - 0.111111111111111*x - 0.910239226626837*3.0^(-1.0 - x)
-0.111111111111111 + 0.101137691847426*log(3^(x + 1) + 9) - 0.111111111111111*x - 0.910239226626837*3.0^(-1.0 - x)
Unión de expresiones racionales
[src]
-1 - x / 1 + x\
- 9*3 + (-1 - x)*log(3) + log\9 + 3 /
-----------------------------------------------
9*log(3)
$$\frac{- 9 \cdot 3^{- x - 1} + \left(- x - 1\right) \log{\left(3 \right)} + \log{\left(3^{x + 1} + 9 \right)}}{9 \log{\left(3 \right)}}$$
(-9*3^(-1 - x) + (-1 - x)*log(3) + log(9 + 3^(1 + x)))/(9*log(3))
Combinatoria
[src]
/ / x\ -x \
-\- log\9 + 3*3 / + 3*3 + x*log(3) + log(3)/
-----------------------------------------------
9*log(3)
$$- \frac{x \log{\left(3 \right)} - \log{\left(3 \cdot 3^{x} + 9 \right)} + \log{\left(3 \right)} + 3 \cdot 3^{- x}}{9 \log{\left(3 \right)}}$$
-(-log(9 + 3*3^x) + 3*3^(-x) + x*log(3) + log(3))/(9*log(3))
Denominador racional
[src]
2 -1 - x 2 / 1 + x\
- 9*log (3) - 81*3 *log(3) - 9*x*log (3) + 9*log(3)*log\9 + 3 /
------------------------------------------------------------------------
2
81*log (3)
$$\frac{- 81 \cdot 3^{- x - 1} \log{\left(3 \right)} - 9 x \log{\left(3 \right)}^{2} + 9 \log{\left(3 \right)} \log{\left(3^{x + 1} + 9 \right)} - 9 \log{\left(3 \right)}^{2}}{81 \log{\left(3 \right)}^{2}}$$
(-9*log(3)^2 - 81*3^(-1 - x)*log(3) - 9*x*log(3)^2 + 9*log(3)*log(9 + 3^(1 + x)))/(81*log(3)^2)
Potencias
[src]
-1 - x / 1 + x\ 1 x 3 log\9 + 3 / - - - - - ------- + --------------- 9 9 log(3) 9*log(3)
$$- \frac{3^{- x - 1}}{\log{\left(3 \right)}} - \frac{x}{9} + \frac{\log{\left(3^{x + 1} + 9 \right)}}{9 \log{\left(3 \right)}} - \frac{1}{9}$$
-1/9 - x/9 - 3^(-1 - x)/log(3) + log(9 + 3^(1 + x))/(9*log(3))
Denominador común
[src]
-x / x / x\\ x 3 *\-3 + 3 *log\3 + 3 // - - + ------------------------- 9 9*log(3)
$$- \frac{x}{9} + \frac{3^{- x} \left(3^{x} \log{\left(3^{x} + 3 \right)} - 3\right)}{9 \log{\left(3 \right)}}$$
-x/9 + 3^(-x)*(-3 + 3^x*log(3 + 3^x))/(9*log(3))
Parte trigonométrica
[src]
-1 - x / 1 + x\ 1 x 3 log\9 + 3 / - - - - - ------- + --------------- 9 9 log(3) 9*log(3)
$$- \frac{3^{- x - 1}}{\log{\left(3 \right)}} - \frac{x}{9} + \frac{\log{\left(3^{x + 1} + 9 \right)}}{9 \log{\left(3 \right)}} - \frac{1}{9}$$
-1/9 - x/9 - 3^(-1 - x)/log(3) + log(9 + 3^(1 + x))/(9*log(3))
Compilar la expresión
[src]
-x - 1 / x + 1 \ 1 x 3 log\3 + 9/ - - - - - ------- + --------------- 9 9 log(3) 9*log(3)
$$- \frac{3^{- x - 1}}{\log{\left(3 \right)}} - \frac{x}{9} + \frac{\log{\left(3^{x + 1} + 9 \right)}}{9 \log{\left(3 \right)}} - \frac{1}{9}$$
-1/9 - x/9 - 3^(-x - 1)/log(3) + log(3^(x + 1) + 9)/(9*log(3))