Question

\(A=\frac{x-21}{x-6\sqrt{x}+5}+\frac{1}{\sqrt{x}-1}+\frac{1}{5-\sqrt{x}}\)

Rút gọn A

Phiền mọi người giải giúp mình ,mình cần gấp . Cảm ơn

Answer 1

Ta có: \(A=\frac{x-21}{x-6\sqrt{x}+5}+\frac{1}{\sqrt{x}-1}+\frac{1}{5-\sqrt{x}}\)

\(=\frac{x-21}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-5\right)}+\frac{\sqrt{x}-5}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-5\right)}-\frac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-5\right)}\)

\(=\frac{x-21+\sqrt{x}-5-\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-5\right)}\)

\(=\frac{x-25}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-5\right)}\)

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

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