4. a. Rút gọn:
$A=\frac{x²+26x-19}{(x-1)(x+3)}+\frac{2x}{1-x}+$ $\frac{x-3}{x+3}$
$A=\frac{x²+26x-19+2x(2x-1)+(x-3)(x-1)}{(x-1)(x+3)}$
$A=\frac{x²+26x-19+2x²-2x+x²-x-3x+3)}{(x-1)(x+3)}$
$A=\frac{(x²+2x²+x²)+(26x-2x-x-3x)-(19-3)}{(x-1)(x+3)}$
$A=\frac{4x²+20x-16}{(x-1)(x+3)}$
ĐKXĐ: $x\neq1$ ; $x\neq-3$
b.
Thay x=-1 vào A ta có:
$A=\frac{4)(-1)²+20(-1)-16}{(-1-1)(-1+3)}$
$A=\frac{4-20-16}{(-2)2}$
$A=\frac{32}{-4}=\frac{-32}{4}$
Vậy: $A=\frac{-32}{4}$ tại $x=-1 $
c. Rút gọn
$⇔A=\frac{4x²+20x-16}{(x-1)(x+3)}>-3$
$⇔A=\frac{4x²+20x-16}{(x-1)(x+3)}>\frac{-3(x-1)(x+3)}{(x-1)(x+3)}$
$⇔A=4x²+20x-16>-3(x-1)(x+3)$
$⇔A=4x²+20x-16>-3x²-9x+3x+3$
$⇔A=(4x²+3x²)+(20x+9x-3x)-(16+3)>0$
$⇔A=7x²+26x-19>0$
(Câu này tui thua) ^_^ So sorry
