Phương trình một ẩn x+5/x^2-5x-x+25/2x^2-50=x-5/2x^2+10x 02/11/2021 Bởi Melody Phương trình một ẩn x+5/x^2-5x-x+25/2x^2-50=x-5/2x^2+10x
$\frac{x+5}{x^2-5x}$ -$\frac{x+25}{2x^2-50}$ =$\frac{x-5}{2x^2+10x}$⇔$\frac{x+5}{x^2-5x}$ -$\frac{x+25}{2x^2-50}$ -$\frac{x-5}{2x^2+10x}$=0⇔$\frac{x+5}{x(x-5)}$ -$\frac{x+25}{2(x^2-25)}$- $\frac{x-5}{2x(x+5)}$=0⇔$\frac{x+5}{x(x-5)}$ -$\frac{x+25}{2(x-5)(x+5)}$- $\frac{x-5}{2x(x+5)}$=0⇔$\frac{2(x+5)(x+5)-x(x+25)-(x-5)(x-5)}{2x(x-5)(x+5)}$ =0 đk:x khác ±5;0⇔2(x+5)(x+5)-x(x+25)-(x-5)(x-5)=0⇔2x²+20x+50-x²-25x-x²+10x-25=0⇔5x+25=0⇔5x=-25⇔x=-5(loại)Vậy S = rỗng Bình luận
$\frac{x+5}{x^2-5x}$ -$\frac{x+25}{2x^2-50}$ =$\frac{x-5}{2x^2+10x}$
⇔$\frac{x+5}{x^2-5x}$ -$\frac{x+25}{2x^2-50}$ -$\frac{x-5}{2x^2+10x}$=0
⇔$\frac{x+5}{x(x-5)}$ -$\frac{x+25}{2(x^2-25)}$- $\frac{x-5}{2x(x+5)}$=0
⇔$\frac{x+5}{x(x-5)}$ -$\frac{x+25}{2(x-5)(x+5)}$- $\frac{x-5}{2x(x+5)}$=0
⇔$\frac{2(x+5)(x+5)-x(x+25)-(x-5)(x-5)}{2x(x-5)(x+5)}$ =0 đk:x khác ±5;0
⇔2(x+5)(x+5)-x(x+25)-(x-5)(x-5)=0
⇔2x²+20x+50-x²-25x-x²+10x-25=0
⇔5x+25=0
⇔5x=-25
⇔x=-5(loại)
Vậy S = rỗng