Bạn tham khảo:
Đáp án:
a/ $S =$ { $-66$ }
b/ $S =$ { $-60$ }
Giải thích các bước giải:
a/ $\dfrac{x+1}{65} + \dfrac{x+3}{63} = \dfrac{x+5}{61} + \dfrac{x+7}{ 59}$
$⇔ \dfrac{x+1}{65} + \dfrac{x+3}{63}+2 = \dfrac{x+5}{61} + \dfrac{x+7}{ 59} + 2$
$⇔ \dfrac{x+1}{65} + \dfrac{x+3}{63} + 1 + 1 = \dfrac{x+5}{61} + \dfrac{x+7}{ 59} + 1 + 1$
$⇔ (\dfrac{x+1}{65}+1) + (\dfrac{x+3}{63}+1) = (\dfrac{x+5}{61}+1) + (\dfrac{x+7}{ 59}+1)$
$⇔ \dfrac{x+66}{65} + \dfrac{x+66}{63} = \dfrac{x+5}{66} + \dfrac{x+66}{ 59}$
$⇔ \dfrac{x+66}{65} + \dfrac{x+66}{63} - \dfrac{x+5}{66} - \dfrac{x+66}{ 59} = 0 $
$⇔ ( x + 66 )( \dfrac{1}{65} + \dfrac{1}{63} - \dfrac{1}{66} - \dfrac{1}{ 59} ) = 0$
Vì $ \dfrac{1}{65} + \dfrac{1}{63} - \dfrac{1}{66} - \dfrac{1}{ 59} ≠ 0$
$⇔ x + 66 = 0 $
$⇔ x = -66$
$S =$ { $-66$ }
b/ $\dfrac{x+29}{31} - \dfrac{x+27}{33} = \dfrac{x+17}{43} - \dfrac{x+15}{45}$
$⇔ \dfrac{x+29}{31} - \dfrac{x+27}{33} + 2 = \dfrac{x+17}{43} - \dfrac{x+15}{45} + 2$
$⇔ \dfrac{x+29}{31} - \dfrac{x+27}{33} + 1 + 1 = \dfrac{x+17}{43} - \dfrac{x+15}{45} + 1 + 1$
$⇔ (\dfrac{x+29}{31}+1) - (\dfrac{x+27}{33}+1) = (\dfrac{x+17}{43}+1) - (\dfrac{x+15}{45}+1)$
$⇔ \dfrac{x+60}{31} - \dfrac{x+60}{33} = \dfrac{x+60}{43} - \dfrac{x+60}{45}$
$⇔ \dfrac{x+60}{31} - \dfrac{x+60}{33} - \dfrac{x+60}{43} + \dfrac{x+60}{45} = 0$
$⇔ ( x + 60 ) ( \dfrac{1}{31} - \dfrac{1}{33} - \dfrac{1}{43} + \dfrac{1}{45} ) = 0$
Vì $\dfrac{1}{31} - \dfrac{1}{33} - \dfrac{1}{43} + \dfrac{1}{45} ≠ 0$
$⇔ x + 60 = 0 $
$⇔ x = -60$
$S =$ { $-60$ }
