Question

Упростите выражение:
$(frac{2a+1}{a^2-9})^-1 *( frac{4a}{2a-1}- frac{12a+1}{2a^2+5a-3})$

Answer 1

1)4a/(2a-1)-(12a+1)/[(2a-1)(a+3)]=(4a²+12a-12a-1)/[(2a-1)(a+3)]=
=(4a²-1)/[(2a-1)(a+3)]=(2a-1)(2a+1)/[(2a-1)(a+3)]=(2a+1)/(a+3)
2)(a-3)(a+3)/(2a+1)*(2a+1)/(a+3)=(a-3)

Answer 2

$frac{ a^{2}-9 }{2a+1}$·$(frac{4a}{2a-1} - frac{12a+1}{(2a-1)(a+3)})$ = $frac{(a-3)(a+3)}{2a+1}$·$frac{4a^{2}+12a-12a-1 }{(2a-1)(a+3)}$ = $frac{(a-3)(4 a^{2} -1)}{4a^{2}-1 }$ = a-3