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B=\(\left(\dfrac{x}{x^2-25}-\dfrac{x-5}{x^2+5x}\right):\dfrac{2x-5}{x^2+5x}+\dfrac{x}{5-x}\)
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15 tháng 11 2023
ĐKXĐ: \(x\notin\left\{0;-5\right\}\)
\(A=\dfrac{x^2}{5x+25}+\dfrac{2\left(x-5\right)}{x}+\dfrac{50+5x}{x\left(x+5\right)}\)
\(=\dfrac{x^2}{5\left(x+5\right)}+\dfrac{2\left(x-5\right)}{x}+\dfrac{5x+50}{x\left(x+5\right)}\)
\(=\dfrac{x^3+2\cdot5\left(x-5\right)\left(x+5\right)+5\left(5x+50\right)}{5x\left(x+5\right)}\)
\(=\dfrac{x^3+10x^2-250+25x+250}{5x\left(x+5\right)}\)
\(=\dfrac{x^3+10x^2+25x}{5x\left(x+5\right)}=\dfrac{x\left(x^2+10x+25\right)}{5x\left(x+5\right)}\)
\(=\dfrac{\left(x+5\right)^2}{5\left(x+5\right)}=\dfrac{x+5}{5}\)
15 tháng 11 2023
\(A=\dfrac{x^2}{5x+25}+\dfrac{2\left(x-5\right)}{x}+\dfrac{50+5x}{x\left(x+5\right)}\left(ĐKXĐ:x\ne0;x\ne-5\right)\)
\(A=\dfrac{x^2}{5\left(x+5\right)}+\dfrac{2\left(x-5\right)}{x}+\dfrac{50+5x}{x\left(x+5\right)}\)
\(A=\dfrac{x^2.x}{5x\left(x+5\right)}+\dfrac{2.5\left(x+5\right)\left(x-5\right)}{5x\left(x+5\right)}+\dfrac{5\left(50+5x\right)}{5x\left(x+5\right)}\)
\(A=\dfrac{x^3}{5x\left(x+5\right)}+\dfrac{10.\left(x^2-25\right)}{5x\left(x+5\right)}+\dfrac{250+25x}{5x\left(x+5\right)}\)
\(A=\dfrac{x^3}{5x\left(x+5\right)}+\dfrac{10x^2-250}{5x\left(x+5\right)}+\dfrac{250+25x}{5x\left(x+5\right)}\)
\(A=\dfrac{x^3+10x^2-250+250+25x}{5x\left(x+5\right)}\)
\(A=\dfrac{x^3+10x^2+25x}{5x\left(x+5\right)}\)
\(A=\dfrac{x\left(x^2+10x+25\right)}{5x\left(x+5\right)}\)
\(A=\dfrac{\left(x+5\right)^2}{5\left(x+5\right)}\)
\(A=\dfrac{x+5}{5}\)
25 tháng 2 2023
Bài 2:
a: \(=2x^4-x^3-10x^2-2x^3+x^2+10x=2x^3-3x^3-9x^2+10x\)
b: \(=\left(x^2-15x\right)\left(x^2-7x+3\right)\)
\(=x^4-7x^3+3x^2-15x^3+105x^2-45x\)
\(=x^4-22x^3+108x^2-45x\)
c: \(=12x^5-18x^4+30x^3-24x^2\)
d: \(=-3x^6+2.4x^5-1.2x^4+1.8x^2\)
KV
7 tháng 1 2023
1) \(\dfrac{15-5x}{5x^2-15x}=\dfrac{5\left(3-x\right)}{5x\left(x-3\right)}=-\dfrac{5\left(x-3\right)}{5x\left(x-3\right)}=-\dfrac{1}{x}\)
Chọn A
2) \(\dfrac{x\left(x-5\right)}{x^2+25}=\dfrac{x\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}=\dfrac{x}{x+5}\)
\(A=0\Leftrightarrow\dfrac{x}{x+5}=0\Leftrightarrow x=0\)
Chọn B
3) \(\dfrac{2x-5}{5-2x}=-\dfrac{5-2x}{5-2x}=-1\)
Chọn D
4 tháng 7 2023
a: ĐKXĐ: x<>0; x<>5; x<>5/2; x<>-5
b: \(M=\left(\dfrac{x}{\left(x-5\right)\left(x+5\right)}-\dfrac{x-5}{x\left(x+5\right)}\right):\dfrac{2x-5}{x\left(x+5\right)}\)
\(=\dfrac{x^2-x^2+10x-25}{x\left(x-5\right)\left(x+5\right)}\cdot\dfrac{x\left(x+5\right)}{2x-5}=\dfrac{1}{x-5}\)
12 tháng 11 2021
a: \(P=\dfrac{x\left(x+2\right)}{2\left(x+5\right)}+\dfrac{x-5}{x}-\dfrac{5x-50}{2x\left(x+5\right)}\)
\(=\dfrac{x^3+2x^2+2x^2-50-5x+50}{2x\left(x+5\right)}\)
\(=\dfrac{x^3+4x^2-5x}{2x\left(x+5\right)}\)
\(=\dfrac{x\left(x+5\right)\left(x-1\right)}{2x\left(x+5\right)}=\dfrac{x-1}{2}\)
30 tháng 11 2021
b: \(B=\dfrac{x^2-3x+2x^2+6x-3x^2-9}{x^2-9}=\dfrac{3x-9}{\left(x-3\right)\left(x+3\right)}=\dfrac{3}{x+3}\)
30 tháng 11 2021
b: \(B=\dfrac{x^2-3x+2x^2+6x-3x^2-9}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{3x-9}{\left(x-3\right)\left(x+3\right)}=\dfrac{3}{x+3}\)
\(B=\left(\dfrac{x}{x^2-25}-\dfrac{x-5}{x^2+5x}\right):\dfrac{2x-5}{x^2+5x}+\dfrac{x}{5-x}\) (1).
Đkxđ: \(x\ne\pm5;\)
(1) \(=\left(\dfrac{x}{\left(x+5\right)\left(x-5\right)}-\dfrac{x-5}{x\left(x+5\right)}\right):\dfrac{2x-5}{x\left(x+5\right)}+\dfrac{x}{5-x}\)
\(=\left(\dfrac{x^2-\left(x-5\right)\left(x-5\right)}{x\left(x+5\right)\left(x-5\right)}\right):\dfrac{2x-5}{x\left(x+5\right)}+\dfrac{x}{5-x}\)
\(=\dfrac{25}{x\left(x+5\right)\left(x-5\right)}.\dfrac{x\left(x+5\right)}{2x-5}-\dfrac{x}{x-5}\)
\(=\dfrac{25}{\left(x-5\right)\left(2x-5\right)}-\dfrac{x}{x-5}\)
\(=\dfrac{25-x\left(2x-5\right)}{\left(x-5\right)\left(2x-5\right)}\)
\(=\dfrac{25-2x^2+5x}{\left(x-5\right)\left(2x-5\right)}\)