Question

Rút gọn biểu thức A = \(\dfrac{8+x\left(1+\sqrt{x-2\sqrt{x}+1}\right)}{\left(x-4\right)\left(x-2\sqrt{x}+4\right)}\) + \(\dfrac{x-3\sqrt{x}}{2\left(x-\sqrt{x}-6\right)}\) với x>1, x ≠ 4, x ≠ 9

Answer 1

\(A=\dfrac{8+\left(\sqrt{x}-1\right)x}{\left(\sqrt{x}-2\right)\left(x-2\sqrt{x}+4\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}}{2\left(\sqrt{x}-2\right)}\)

\(=\dfrac{16+2x\sqrt{x}-2x+\sqrt{x}\left(x\sqrt{x}+8\right)}{2\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)\left(x-2\sqrt{x}+4\right)}\)

\(=\dfrac{x^2+2x\sqrt{x}-2x+8\sqrt{x}+16}{2\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)\left(x-2\sqrt{x}+4\right)}\)