Bài 1:
a) Rút gọn:
\(A=\left(\frac{3-x}{x+3}.\frac{x^2+6x+9}{x^2-9}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(\frac{3-x}{x+3}.\frac{\left(x+3\right)^2}{\left(x-3\right).\left(x+3\right)}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(\frac{\left(3-x\right).\left(x+3\right)^2}{\left(x+3\right).\left(x-3\right).\left(x+3\right)}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(\frac{-\left(x-3\right).\left(x+3\right)^2}{\left(x+3\right)^2.\left(x-3\right)}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(-1+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(\frac{-1.\left(x+3\right)}{x+3}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(\frac{-x-3}{x+3}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(\frac{-x-3+x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\frac{-3}{x+3}:\frac{3x^2}{x+3}\)
\(A=\frac{-3}{x+3}.\frac{x+3}{3x^2}\)
\(A=\frac{-3.\left(x+3\right)}{\left(x+3\right).3x^2}\)
\(A=\frac{-1}{x^2}.\)
b) Ta có:
\(\left|x\right|=-\frac{1}{2}\)
Vì \(\left|x\right|\ge0\) \(\forall x.\)
\(\Rightarrow\left|x\right|>-\frac{1}{2}\)
\(\Rightarrow\left|x\right|\ne-\frac{1}{2}\)
\(\Rightarrow x\in\varnothing.\)
Vậy biểu thức A không có giá trị tại \(\left|x\right|=-\frac{1}{2}.\)
Chúc bạn học tốt!
Bài 1: Cho biểu thức: \(A=\left(\frac{3-x}{x+3}\cdot\frac{x^2+6x+9}{x^2-9}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
a) Rút gọn biểu thức \(A\)
\(A=\left(\frac{3-x}{x+3}\cdot\frac{x^2+6x+9}{x^2-9}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(\frac{-\left(x-3\right)\left(x+3\right)\left(x+3\right)}{\left(x+3\right)\left(x+3\right)\left(x-3\right)}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(-1+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\left(\frac{-x-3}{x+3}+\frac{x}{x+3}\right):\frac{3x^2}{x+3}\)
\(A=\frac{-3}{x+3}:\frac{3x^2}{x+3}\)
\(A=\frac{-3}{x+3}\cdot\frac{x+3}{3x^2}\)
\(A=\frac{-3\left(x+3\right)}{\left(x+3\right)3x^2}\)
\(A=\frac{-1}{x^2}\)
