5.
theo đề bài ta có :
a/b = c/d
⇒ad = bc
a)
a-b/b = c-d/d
⇒ba - b²/b = bc-bd/d
⇒b(a-b)/b = bc-bd/d
⇒a-b = ad - bd/d
⇒a-b = d(a-b)/d
⇒VT = VP
b)
(2a+3b)/(2a-3b) =( 2c+3d)/(2c-3d)
⇒(2a+3b)(2c-3d) = (2c+3d)(2a-3b)
⇒4ac-6ad+6bc-9bd = 4ac-6bc+6ad-9bd
⇒4ac-6bc+6ad-9bd = 4ac-6bc+6ad-9bd
⇒VT=VP
c)
ac/bd = (a² - c² )/ (b² - d²)
⇒ac(b² - d²) = bd(a² - c²)
⇒acb² - acd² = a²bd - c²bd
⇒abbc - addc = abad - bcbd
⇒abbc - bcdc = abbc - bcdc
⇒VT = VP
6.
theo đề bài ta có :
b²= ac ⇒a/b = b/c
c²=bd⇒b/c=c/d
⇒a/b=b/c=c/d = (a+b-c)/(b+c-d)
⇒a³/b³=b³/c³=c³/d³ = (a+b-c/b+c-d)³=(a³+b³-c³)/(b³+c³-d³)
⇒(a³+b³-c³)/(b³+c³-d³)=(a+b-c/b+c-d)³
⇒(a³+b³-c³)/(b³+c³-d³)=(a+b-c)³/(b+c-d)³ (đpcm)
