Question

Calcular essa função exponencial.

Por favooooor me ajudeeeeeeem!

Answer 1

$\dfrac{2^{x}+2^{x+1}-5\cdot2^{x+2}}{2^{x}-2^{x+3}-17\cdot2^{x}}=\dfrac{2^{x}+2^{x}\cdot2^{1}-5\cdot2^{x}\cdot2^{2}}{2^{x}-2^{x}\cdot2^{3}-17\cdot2^{x}}\\\\\\\dfrac{2^{x}+2^{x+1}-5\cdot2^{x+2}}{2^{x}-2^{x+3}-17\cdot2^{x}}=\dfrac{2^{x}+2^{x}\cdot2-5\cdot2^{x}\cdot4}{2^{x}-2^{x}\cdot8-17\cdot2^{x}}\\\\\\\dfrac{2^{x}+2^{x+1}-5\cdot2^{x+2}}{2^{x}-2^{x+3}-17\cdot2^{x}}=\dfrac{2^{x}+2\cdot2^{x}-20\cdot2^{x}}{2^{x}-8\cdot2^{x}-17\cdot2^{x}}$

Vamos colocar a potência com menor expoente aparente no numerador e denominador (2^x):

$\dfrac{2^{x}+2^{x+1}-5\cdot2^{x+2}}{2^{x}-2^{x+3}-17\cdot2^{x}}=\dfrac{2^{x}\cdot(1+2-20)}{2^{x}\cdot(1-8-17)}$

Cancelando 2^x:

$\dfrac{2^{x}+2^{x+1}-5\cdot2^{x+2}}{2^{x}-2^{x+3}-17\cdot2^{x}}=\dfrac{1+2-20}{1-8-17}\\\\\\\dfrac{2^{x}+2^{x+1}-5\cdot2^{x+2}}{2^{x}-2^{x+3}-17\cdot2^{x}}=\dfrac{(-17)}{(-24)}\\\\\\\boxed{\boxed{\dfrac{2^{x}+2^{x+1}-5\cdot2^{x+2}}{2^{x}-2^{x+3}-17\cdot2^{x}}=\dfrac{17}{24}}}$