Question

Cho biểu thức:  P=\(\frac{x\sqrt{x}+26\sqrt{x}-19}{x+2\sqrt{x}-3}-\frac{2\sqrt{x}}{\sqrt{x}1}+\frac{\sqrt{x}-3}{\sqrt{x}+3}\)

a) Rút gọn

b) Tính P khi x=\(7-4\sqrt{3}\)

c) Tìm giá trị lớn nhất

Answer 1

ĐKXĐ:  \(x\ge0;x\ne1\)

mk chỉnh lại đề, đúng thì bạn tham khảo

\(P=\frac{x+26\sqrt{x}-19}{x+2\sqrt{x}-3}-\frac{2\sqrt{x}}{\sqrt{x}-1}+\frac{\sqrt{x}-3}{\sqrt{x}+3}\)

\(=\frac{x+26\sqrt{x}-19}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\frac{2\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}+\frac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)

\(=\frac{x+26\sqrt{x}-19}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}-\frac{2x+6\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}+\frac{x-2\sqrt{x}-3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)

\(=\frac{18\sqrt{x}-22}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}\)