Question

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

a) Rút gọn bt

b)Tính gt của A tại x=9/4

c)Tìm x để A<1

d) Tìm x để A đạt gt nguyên

MONG CÁC BẠN GIẢI NHANH GIÚP 

Answer 1

ĐK : tự ghi nha

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

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

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

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

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

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

\(A=\frac{x-\sqrt{x}+1-\left(x-2\sqrt{x}+1\right)}{\sqrt{x}-1}\)

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

\(A=\frac{\sqrt{x}}{\sqrt{x}-1}\)