\(\dfrac{x+5}{x^2-5x}-\dfrac{x-5}{2x^2+10x}=\dfrac{x+25}{2x^2-50}\)
\(\dfrac{x+5}{x\left(x-5\right)}-\dfrac{x-5}{2x\left(x+5\right)}=\dfrac{x+5}{2\left(x-5\right)\left(x+5\right)}\)
dkxd : x ≠ 0
x ≠ 5
x ≠ -5
MTC : 2x(x - 5)(x + 5)
Quy đồng mẫu thức hai vế của phương trình :
⇒ \(\dfrac{2\left(x-5\right)\left(x+5\right)}{2x\left(x-5\right)\left(x+5\right)}-\dfrac{\left(x-5\right)\left(x+5\right)}{2x\left(x-5\right)\left(x+5\right)}\) = \(\dfrac{x\left(x+25\right)}{2x\left(x-5\right)\left(x+5\right)}\)
Suy ra : 2(x - 5)(x + 5) - (x - 5)(x + 5) = x(x + 25)
\(\Leftrightarrow\) 2(x2 - 25) - (x2 - 25) = x2 + 25x
\(\Leftrightarrow\) 2x2 - 50 - x2 + 25 - x2 - 25x = 0
\(\Leftrightarrow\) -25 - 25x = 0
\(\Leftrightarrow\) -25x = 25
\(\Leftrightarrow\) x = \(\dfrac{25}{-25}=-1\) (thỏa mãn)
Vậy S = \(\left\{-1\right\}\)
Chúc bạn học tốt
Ta có: \(\dfrac{x+5}{x^2-5x}-\dfrac{x-5}{2x^2+10x}=\dfrac{x+25}{2x^2-50}\)
\(\Leftrightarrow\dfrac{2\left(x+5\right)^2}{2x\left(x+5\right)\left(x-5\right)}-\dfrac{\left(x-5\right)^2}{2x\left(x+5\right)\left(x-5\right)}=\dfrac{x\left(x+25\right)}{2x\left(x+5\right)\left(x-5\right)}\)
Suy ra: \(2\left(x^2+10x+25\right)-\left(x^2-10x+25\right)=x^2+25x\)
\(\Leftrightarrow2x^2+20x+50-x^2+10x-25-x^2-25x=0\)
\(\Leftrightarrow15x+25=0\)
\(\Leftrightarrow15x=-25\)
hay \(x=-\dfrac{5}{3}\)(thỏa ĐK)