Question

7. ¿A cuál de las siguientes expresiones es igual (1/(1+(1/(1+(1/(1+(1/x))))))) ?2x+1х3x+2b. 2x+1C. 3x+24x+3d.3x+2a. x+1

Answer 1

$\frac{2x\text{ + 1}}{3x\text{ + 2}}$

Aquí, queremos evaluar las expresiones entre paréntesis;

(1/(1+(1/(1+(1/(1+(1/x)))))))

= (1/(1+(1/(1+(1/(1+1/x))))))

= (1/(1+(1/(1+(1/(x+1)/x))))

= (1/(1+(1/(1+(x/(x+1))))

= (1/(1+(1/((x+1+x)/(x+1))))

= (1/(1+(1/((2x+1/(x+1)))

= (1/(1+(x+1/(2x+1)

= (1/(2x + 1+(x+1/(2x+1)

= (1/(3x+2)/(2x+1)

= (2x+1)/(3x+2)