Đáp án:Ta có :
$\frac{1}{7}$+ $\frac{1}{23}$ -$\frac{1}{1009}$ +$\frac{1}{7}$ .$\frac{1}{23}$ .$\frac{1}{1009}$ = $\frac{7063}{162449}$ +$\frac{23207}{162449}$ -$\frac{161}{162449}$ +$\frac{1}{162449}$ =$\frac{30110}{162449}$
⇒
$\frac{1}{7}$+ $\frac{1}{23}$ -$\frac{1}{1009}$ =$\frac{30110}{162449}$ -$\frac{1}{162449}$ =$\frac{30109}{30110}$
⇒(1/7+1/23-1/1009):(1/23+1/7-1/1009+1/7.1/23.1/1009)=$\frac{30109:162449}{30110:162449}$
=$\frac{30109}{30110}$
Mà$\frac{1}{30.1009-160}$ =$\frac{1}{30110}$
⇒A=(1/7+1/23-1/1009):(1/23+1/7-1/1009+1/7.1/23.1/1009)+1:(30.1009-160)=$\frac{30109}{30110}$ +$\frac{1}{30110}$ =1
Giải thích các bước giải:
