Hướng dẫn trả lời:
Bài tập 1:
$\text{Câu a) $\dfrac{64x^3+1}{16x^2-1}$ = $\dfrac{A}{4x-1}$.}$
$\text{⇒ ($64x^3+1$).(4x - 1) = ($16x^2-1$).A.}$
$\text{⇒ [$(4x)^3+1^3$].(4x - 1) = [$(4x)^2-1^2$].A.}$
$\text{⇒ (4x + 1).[$(4x)^2$ - 4x.1 + $1^2$].(4x - 1) = (4x + 1).(4x - 1).A.}$
$\text{⇒ (4x + 1).($16x^2$ - 4x + 1).(4x - 1) = (4x + 1).(4x - 1).A.}$
$\text{⇒ A = $\dfrac{(4x + 1).(4x - 1).(16x^2-4x+1)}{(4x + 1).(4x - 1)}$.}$
$\text{⇒ A = $16x^2$ - 4x + 1.}$
$\text{Vậy A = $16x^2$ - 4x + 1.}$
$\text{Câu b) $\dfrac{5x-2}{B}$ = $\dfrac{10x^2-29x+10}{-10x^2+27x-5}$.}$
$\text{⇒ (5x - 2).($-10x^2$ + 27x - 5) = B.($10x^2$ - 29x + 10).}$
$\text{⇒ (5x - 2). -($10x^2$ - 27x + 5) = B.($10x^2$ - 29x + 10).}$
$\text{⇒ (5x - 2). -($10x^2$ - 2x - 25x + 5) = B.($10x^2$ - 25x - 4x + 10).}$
$\text{⇒ (5x - 2).(2x - 5). -(5x -1) = B.(5x - 2).(2x - 5).}$
$\text{⇒ B = $\dfrac{(5x-2).(2x-5).-(5x - 1)}{(5x - 2).(2x-5)}$.}$
$\text{⇒ B = -(5x - 1) = -5x + 1.}$
$\text{Vậy B = -5x + 1.}$
