Đáp án:
$b. B = 6x^{2} - 3x$
$c. B = x$
$d. B = x^{3} - 3x^{2}y + 3xy^{2} - y^{3}$
Giải thích các bước giải:
$b. \frac{x^{2}+8}{2x-1} = \frac{3x^{3}+24x}{B}$ $( x \ne \frac{1}{2} , B \ne 0 )$
⇔ $\frac{x^{2}+8}{2x-1} = \frac{3x(x^{2}+8)}{B}$
⇔ $\frac{1}{2x-1} = \frac{3x}{B}$
⇔ $B = 3x( 2x - 1 )$
⇔ $B = 6x^{2} - 3x$
$c. \frac{B}{x-y} = \frac{3x^{2}-3xy}{3(y-x)^{2}}$ $( x \ne y )$
⇔ $\frac{B}{x-y} = \frac{3x(x-y)}{3(x-y)^{2}}$
⇔ $\frac{B}{x-y} = \frac{x}{x-y}$
⇔ $B = x$
$d. \frac{-x^{2}+2xy-y^{2}}{x+y} = \frac{B}{y^{2}-x^{2}}$ $( x \ne y , x \ne - y )$
⇔ $\frac{-(x^{2}-2xy+y^{2})}{x+y} = \frac{B}{(y-x)(y+x)}$
⇔ $\frac{-(x-y)^{2}}{x+y} = \frac{B}{-(x-y)(x+y)}$
⇔ $- ( x - y )^{2} = - \frac{B}{x-y}$
⇔ $B = ( x - y )^{3}$
⇔ $B = x^{3} - 3xy( x - y ) - y^{3}$
⇔ $B = x^{3} - 3x^{2}y + 3xy^{2} - y^{3}$
