Rút gọn biểu thức A: Giúp mình với ạ $\frac{√x +1}{1-√x}$ -$\frac{3√x-1}{x-1}$ = A 19/08/2021 Bởi Amara Rút gọn biểu thức A: Giúp mình với ạ $\frac{√x +1}{1-√x}$ -$\frac{3√x-1}{x-1}$ = A
Đáp án: Ta có : A = $\frac{\sqrt[]{x}+ 1}{1-\sqrt[]{x} }$ – $\frac{3\sqrt[]{x} – 1}{x- 1}$ A = $\frac{-\sqrt[]{x} – 1}{\sqrt[]{x} – 1}$ – $\frac{3\sqrt[]{x} – 1}{x- 1}$ A = $\frac{-\sqrt[]{x} – 1}{\sqrt[]{x} – 1}$ – $\frac{3\sqrt[]{x} – 1}{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$ A = $\frac{(-\sqrt[]{x} – 1).\sqrt[]{x} + 1 )}{(\sqrt[]{x} – 1)(\sqrt[]{x} + 1 )}$ – $\frac{3\sqrt[]{x} – 1}{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$ A = $\frac{-(\sqrt[]{x}+1)^{2} – 3\sqrt[]{x} + 1 }{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$ A = $\frac{-x – 2\sqrt[]{x} – 1 – 3\sqrt[]{x} + 1 }{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$ A = $\frac{-x – 5\sqrt[]{x} }{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$ Bình luận
Đáp án: $A=\dfrac{\sqrt[]{x} +1}{1 -\sqrt[]{x}} – \dfrac{3\sqrt[]{x} -1}{x-1} $ $=\dfrac{-(\sqrt[]{x}+1)(\sqrt[]{x}+1)}{(\sqrt[]{x}-1)(\sqrt[]{x}+1)} – \dfrac{3\sqrt[]{x}-1}{(\sqrt[]{x}-1)(\sqrt[]{x}+1)}$ $= \dfrac{-(\sqrt[]{x}+1)^2 – 3\sqrt[]{x} +1}{(\sqrt[]{x}-1)(\sqrt[]{x} +1)}$ $=\dfrac{-(x+2\sqrt[]{x} +1) -3\sqrt[]{x}+1}{(\sqrt[]{x}-1)(\sqrt[]{x} +1)}$ $= \dfrac{-x -2\sqrt[]{x} -1 -3\sqrt[]{x} +1}{(\sqrt[]{x}-1)(\sqrt[]{x} +1)}$ $= \dfrac{-x -5\sqrt[]{x} }{(\sqrt[]{x}-1)(\sqrt[]{x}+1)}$ Bình luận
Đáp án:
Ta có :
A = $\frac{\sqrt[]{x}+ 1}{1-\sqrt[]{x} }$ – $\frac{3\sqrt[]{x} – 1}{x- 1}$
A = $\frac{-\sqrt[]{x} – 1}{\sqrt[]{x} – 1}$ – $\frac{3\sqrt[]{x} – 1}{x- 1}$
A = $\frac{-\sqrt[]{x} – 1}{\sqrt[]{x} – 1}$ – $\frac{3\sqrt[]{x} – 1}{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$
A = $\frac{(-\sqrt[]{x} – 1).\sqrt[]{x} + 1 )}{(\sqrt[]{x} – 1)(\sqrt[]{x} + 1 )}$ – $\frac{3\sqrt[]{x} – 1}{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$
A = $\frac{-(\sqrt[]{x}+1)^{2} – 3\sqrt[]{x} + 1 }{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$
A = $\frac{-x – 2\sqrt[]{x} – 1 – 3\sqrt[]{x} + 1 }{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$
A = $\frac{-x – 5\sqrt[]{x} }{( \sqrt[]{x} – 1 ).( \sqrt[]{x} + 1 )}$
Đáp án:
$A=\dfrac{\sqrt[]{x} +1}{1 -\sqrt[]{x}} – \dfrac{3\sqrt[]{x} -1}{x-1} $
$=\dfrac{-(\sqrt[]{x}+1)(\sqrt[]{x}+1)}{(\sqrt[]{x}-1)(\sqrt[]{x}+1)} – \dfrac{3\sqrt[]{x}-1}{(\sqrt[]{x}-1)(\sqrt[]{x}+1)}$
$= \dfrac{-(\sqrt[]{x}+1)^2 – 3\sqrt[]{x} +1}{(\sqrt[]{x}-1)(\sqrt[]{x} +1)}$
$=\dfrac{-(x+2\sqrt[]{x} +1) -3\sqrt[]{x}+1}{(\sqrt[]{x}-1)(\sqrt[]{x} +1)}$
$= \dfrac{-x -2\sqrt[]{x} -1 -3\sqrt[]{x} +1}{(\sqrt[]{x}-1)(\sqrt[]{x} +1)}$
$= \dfrac{-x -5\sqrt[]{x} }{(\sqrt[]{x}-1)(\sqrt[]{x}+1)}$