A =[tex]\frac{x^2 + 2x}{2x + 10} + \frac{x - 5}{x} - \frac{5x - 50}{2x(x + 5)}[/tex]
a) Rút gọn A
b) Rìm x để A = 1; A = - 3
c) Tìm GTNN của biểu thức P = 2( x + 2 )A
DK: [tex]\left\{\begin{matrix} x\neq 0 & \\ x+5\neq 0 & \end{matrix}\right.\\\Leftrightarrow \left\{\begin{matrix} x\neq 0 & \\ x\neq -5& \end{matrix}\right.[/tex]
a)[tex]A =\frac{x^2 + 2x}{2x + 10} + \frac{x - 5}{x} - \frac{5x - 50}{2x(x + 5)}\\=\frac{x(x+2)}{2(x+5)}+ \frac{x - 5}{x}-\frac{5(x-10)}{2x(x + 5)}\\=\frac{x^2(x+2)+2(x-5)(x+5)-5x+50}{2x(x+5)}\\=\frac{x^3+2x^2+2x^2-50-5x+50}{2x(x+5)}\\=\frac{x^3+4x^2-5x}{2x(x+5)}\\=\frac{x(x^2+4x-5)}{2x(x+5)}\\=\frac{x^2-x+5x-5}{2(x+5)}\\=\frac{x(x-1)+5(x-1)}{2(x+5)}\\=\frac{(x+5)(x-1)}{2(x+5)}\\=\frac{x-1}{2}[/tex]
b)Thay vào rồi tìm x
c)[tex]P = 2( x + 2 )A\\=(2x+4)(\frac{x-1}{2})\\=\frac{(2x+4)(x-1)}{2}\\=\frac{2x^2-2x+4x-4}{2}\\=\frac{2x^2+2x-4}{2}\\=\frac{2(x^2+x-2)}{2}\\=x^2+x-2\\=x^2+2.x.\frac{1}{2}+\frac{1}{4}-\frac{9}{4}\\=(x+\frac{1}{2})^2-\frac{9}{4}\geq \frac{-9}{4}[/tex]
Vậy..........
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