Question

\(\dfrac{\sqrt{x}+2}{-\sqrt{x}+2}+\dfrac{3\sqrt{x}-4}{2\sqrt{x}-3}+\dfrac{-7\sqrt{x}+10}{-2x+7\sqrt{x}-6}\)

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Answer 1

\(=\dfrac{-\left(\sqrt{x}+2\right)}{\sqrt{x}-2}+\dfrac{3\sqrt{x}-4}{2\sqrt{x}-3}+\dfrac{7\sqrt{x}-10}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{-\left(2x-3\sqrt{x}+4\sqrt{x}-6\right)+3x-6\sqrt{x}-4\sqrt{x}+8+7\sqrt{x}-10}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)

\(=\dfrac{-2x-\sqrt{x}+6+3x-3\sqrt{x}-2}{\left(2\sqrt{x}-3\right)\cdot\left(\sqrt{x}-2\right)}\)

\(=\dfrac{x-4\sqrt{x}+4}{\left(2\sqrt{x}-3\right)\cdot\left(\sqrt{x}-2\right)}=\dfrac{\sqrt{x}-2}{2\sqrt{x}-3}\)