Question

giải phương trình:\(\frac{2x}{\sqrt{5}-\sqrt{3}}-\frac{2x}{\sqrt{3}+1}=\sqrt{5}+1\)

Answer 1

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

\(\Leftrightarrow\frac{2x\left(\sqrt{5}+\sqrt{3}\right)}{\left(\sqrt{5}\right)^2-\left(\sqrt{3}\right)^2}-\frac{2x\left(\sqrt{3}-1\right)}{\left(\sqrt{3}\right)^2-1}=\sqrt{5}+1\)

\(\Leftrightarrow\frac{2x\left(\sqrt{5}+\sqrt{3}\right)}{5-3}-\frac{2x\left(\sqrt{3}-1\right)}{3-1}=\sqrt{5}+1 \)

\(\Leftrightarrow x\left(\sqrt{5}+\sqrt{3}\right)-x\left(\sqrt{3}-1\right)=\sqrt{5}+1\)

\(\Leftrightarrow\sqrt{5}x+\sqrt{3}x-\sqrt{3}x+x=\sqrt{5}+1\)

\(\Leftrightarrow\sqrt{5}x+x=\sqrt{5}+1\)

\(\Leftrightarrow x\left(\sqrt{5}+1\right)=\sqrt{5}+1\)

\(\Leftrightarrow x=1\)