Question

rút gọn biểu thức sau
\(\frac{15\sqrt{x}-11}{x+2\sqrt{x}-3}-\frac{3\sqrt{x}-2}{\sqrt{x}-1}-\frac{2\sqrt{x}+3}{\sqrt{x}+3}\)

Answer 1

Lời giải:
ĐK: $x\geq 0; x\neq 1$

Đặt biểu thức là $P$

\(P=\frac{15\sqrt{x}-11}{(\sqrt{x}-1)(\sqrt{x}+3)}-\frac{(3\sqrt{x}-2)(\sqrt{x}+3)}{(\sqrt{x}-1)(\sqrt{x}+3)}-\frac{(2\sqrt{x}+3)(\sqrt{x}-1)}{(\sqrt{x}+3)(\sqrt{x}-1)}\)

\(=\frac{15\sqrt{x}-11-(3x+7\sqrt{x}-6)-(2x+\sqrt{x}-3)}{(\sqrt{x}+3)(\sqrt{x}-1)}\)

\(=\frac{-5x+7\sqrt{x}-2}{(\sqrt{x}+3)(\sqrt{x}-1)}=\frac{(\sqrt{x}-1)(-5\sqrt{x}+2)}{(\sqrt{x}-1)(\sqrt{x}+3)}=\frac{2-5\sqrt{x}}{\sqrt{x}+3}\)