Question

[Lê Hà Lâm]

 Giúp mình bài 9 câu c với ạ. Tối nay trước 9h mình phải nộp rồi ạ. Thanks

Answer 1

[Nguyễn Lê Phước Thịnh]

9:

a: ĐKXĐ: \(x\notin\left\{0;-5\right\}\)

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

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

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

\(=\dfrac{x^3+2x^2+2x^2-50+50-5x}{2x\left(x+5\right)}=\dfrac{x^3+4x^2-5x}{2x\left(x+5\right)}\)

\(=\dfrac{x\left(x^2+4x-5\right)}{2x\left(x+5\right)}=\dfrac{\left(x+5\right)\left(x-1\right)}{2\left(x+5\right)}=\dfrac{x-1}{2}\)

b: Khi x=2 thì \(P=\dfrac{2-1}{2}=\dfrac{1}{2}\)

c: \(S=P\cdot\dfrac{2}{x-2}=\dfrac{x-1}{2}\cdot\dfrac{2}{x-2}=\dfrac{x-1}{x-2}=\dfrac{x-2+1}{x-2}=1+\dfrac{1}{x-2}\)

Để S là số nguyên thì \(x-2\in\left\{1;-1\right\}\)

=>\(x\in\left\{3;1\right\}\)

Answer 2

[Lê Hà Lâm]

mình cảm ơn ạ