Question

\((\frac{\sqrt{c}}{\sqrt{c}+2}-\frac{\sqrt{c}}{\sqrt{c}-2}+\frac{4\sqrt{c}-1}{c-4})\cdot\frac{\sqrt{c}+2}{1}\)   rút gọn hộ mk vs mk cần gấp

Answer 1

(đkxđ: \(c\ge0,c\ne4\))

Ta có \(A=\left(\frac{\sqrt{c}}{\sqrt{c}+2}-\frac{\sqrt{c}}{\sqrt{c}-2}+\frac{4\sqrt{c}-1}{c-4}\right).\left(\sqrt{c}+2\right)\)

\(=\frac{\sqrt{c}\left(\sqrt{c}-2\right)-\sqrt{c}\left(\sqrt{c}+2\right)+4\sqrt{c}-1}{\left(\sqrt{c}+2\right)\left(\sqrt{c}-2\right)}\left(\sqrt{c}+2\right)\)

\(=\frac{c-2\sqrt{c}-c-2\sqrt{c}+4\sqrt{c}-1}{\left(\sqrt{c}-2\right)}\)

\(=\frac{1}{2-\sqrt{c}}\)