√x + 3/ √x – 1 – √x +1/ √x – 3 + 3 √x – 1/ x – 4 √x + 3 Rút gọn hộ mik vs 01/07/2021 Bởi Remi √x + 3/ √x – 1 – √x +1/ √x – 3 + 3 √x – 1/ x – 4 √x + 3 Rút gọn hộ mik vs
Đáp án: $\dfrac{3}{\sqrt[]{x}+3}$ Giải thích các bước giải: $\dfrac{\sqrt[]{x}+3}{\sqrt[]{x}-1}-\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}-3}+\dfrac{3\sqrt[]{x}-1}{x-4\sqrt[]{x}+3}$ $=\dfrac{\sqrt[]{x}+3}{\sqrt[]{x}-1}-\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}-3}+\dfrac{3\sqrt[]{x}-1}{(\sqrt[]{x}-1)(\sqrt[]{x}-3)}$ $=\dfrac{(\sqrt[]{x}+3)(\sqrt[]{x}-3)-(\sqrt[]{x}+1)(\sqrt[]{x}-1)+3\sqrt[]{x}-1}{(\sqrt[]{x}-1)(\sqrt[]{x}-3)}$ $=\dfrac{x-9-(x-1)+3\sqrt[]{x}-1}{(\sqrt[]{x}-3)(\sqrt[]{x}+3)}$ $=\dfrac{3(\sqrt[]{x}-3)}{(\sqrt[]{x}-3)(\sqrt[]{x}+3)}$ $=\dfrac{3}{\sqrt[]{x}+3}$ Bình luận
Đáp án:
$\dfrac{3}{\sqrt[]{x}+3}$
Giải thích các bước giải:
$\dfrac{\sqrt[]{x}+3}{\sqrt[]{x}-1}-\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}-3}+\dfrac{3\sqrt[]{x}-1}{x-4\sqrt[]{x}+3}$
$=\dfrac{\sqrt[]{x}+3}{\sqrt[]{x}-1}-\dfrac{\sqrt[]{x}+1}{\sqrt[]{x}-3}+\dfrac{3\sqrt[]{x}-1}{(\sqrt[]{x}-1)(\sqrt[]{x}-3)}$
$=\dfrac{(\sqrt[]{x}+3)(\sqrt[]{x}-3)-(\sqrt[]{x}+1)(\sqrt[]{x}-1)+3\sqrt[]{x}-1}{(\sqrt[]{x}-1)(\sqrt[]{x}-3)}$
$=\dfrac{x-9-(x-1)+3\sqrt[]{x}-1}{(\sqrt[]{x}-3)(\sqrt[]{x}+3)}$
$=\dfrac{3(\sqrt[]{x}-3)}{(\sqrt[]{x}-3)(\sqrt[]{x}+3)}$
$=\dfrac{3}{\sqrt[]{x}+3}$
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