Question

Cho biểu thức

\(A=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)

a. Tìm điều kiện xác định của A

b. rút gọn A

c. tìm x để A=1; A= -3

Answer 1

a) ĐKXĐ : \(x\ne0;-5\)

b) \(A=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)

\(A=\frac{x\left(x^2+2x\right)}{2x\left(x+5\right)}+\frac{2\left(x+5\right)\left(x-5\right)}{2x\left(x+5\right)}+\frac{50-5x}{2x\left(x+5\right)}\)

\(A=\frac{x^3+2x^2+x^2-50+20-5x}{2x\left(x+5\right)}\)

\(A=\frac{x\left(x-1\right)\left(x+5\right)}{2x\left(x+5\right)}\)

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

c) \(A=1\Leftrightarrow\frac{x-1}{2}=1\Leftrightarrow x=3\)( thỏa )

\(A=-3\Leftrightarrow\frac{x-1}{2}=-3\Leftrightarrow x=-5\)( loại )

Answer 2

a, hông biết

b,

\(A=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x.\left(x+5\right)}\)

\(A=\frac{x^2+2x}{2x\left(x+5\right)}+\frac{x-5}{x}+\frac{50-5x}{2x+\left(x+5\right)}\)

\(A=\frac{x\left(x^2+2x\right)}{2x\left(x+5\right)}+\frac{2\left(x+5\right).\left(x-5\right)}{2x\left(x+5\right)}+\frac{50-5x}{2x.\left(x+5\right)}\)

\(A=\frac{x\left(x^2+2x\right)+2\left(x+5\right).\left(x-5\right)+50-5x}{2x.\left(x+5\right)}\)

\(A=\frac{x^3+2x+2\left(x^2-25\right)+50-5x}{2x\left(x+5\right)}\)

\(A=\frac{x^3+2x^2+2x^2-50+50-5x}{2x.\left(x+5\right)}\)

\(A=\frac{x^3+4x^2-5x}{2x.\left(x+5\right)}\)

\(A=\frac{x^2+5x-x-5}{2\left(x+5\right)}\)

\(A=\frac{x.\left(x+5\right)-\left(x+5\right)}{2\left(x+5\right)}\)

\(A=\frac{\left(x+5\right)\left(x-1\right)}{2\left(x+5\right)}\)

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

c,

\(\left[{}\begin{matrix}\frac{x-1}{2}=1\\\frac{x-1}{2}=-3\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x-1=1.2=2\\x-1=-3.2=-6\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=2+1=3\\x=-6+1=-5\end{matrix}\right.\)

Vậy \(x\in\left\{3;-5\right\}\)

Answer 3

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Answer 4

a) \(A=\frac{x^2+2x}{2x+10}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)

\(A=\frac{x^2+2x}{2\left(x+5\right)}+\frac{x-5}{x}+\frac{50-5x}{2x\left(x+5\right)}\)

ĐKXĐ : \(x\ne0;x\ne-5\)

=> A= \(x\left(x^2+2x\right)+2\left(x-5\right)\left(x+5\right)+50-5x\)

<=> A = \(x^3+2x^2+2x^2-50+50-5x\)

<=> A = \(x^3+4x^2-5x\)