\(\frac{144}{x+2}-\frac{100}{x}=2\)
\(\frac{144}{x-2}.x\left(x+2\right)-\frac{100}{x}.x\left(x+2\right)=2.x\left(x+2\right)\)
144x - 100(x + 2) = 2.x(x + 2)
x = 10
=> x = 10
K chắc nhá :w
\(ĐK:x\ne-2;x\ne0\)
\(\frac{144}{x+2}-\frac{100}{x}=2\)
\(\Leftrightarrow\frac{144}{x+2}-\frac{100}{x}-2=0\Leftrightarrow\frac{144x-100x-200-2x^2-4x}{\left(x+2\right)x}=0\)
\(\Leftrightarrow\frac{40x-2x^2-200}{\left(x+2\right)x}=0\Leftrightarrow40x-2x^2-200=0\Leftrightarrow20x-x^2-200=0\)
\(\Leftrightarrow-\left(20x-x^2-200\right)=0\Leftrightarrow x^2-20x+200=0\)
\(\Leftrightarrow\left(x-10\right)^2+100=0\left(\text{vô lí}\right)\)
\(\text{Vậy: pt vô nghiệm}\)
Khoan đã lm lại nhé =(( hơi nhầm 1 chỗ =((
tui lớp 6 nên chỉ biết:
144x/(x+2).x=100.(x+2)/(x+2).x
do x.(x+2) = nhau nên 144x=100.(x+2)
suy ra 100x+200=144x =>44x=200
=> x rỗng (làm bừa vãi đéo bít đúng ko)
\(-ĐKXĐ:\hept{\begin{cases}x+2\ne0\\x\ne0\end{cases}}\Leftrightarrow\hept{\begin{cases}x\ne-2\\x\ne0\end{cases}}\)
-Ta có : \(\frac{144}{x+2}-\frac{100}{x}=2\Leftrightarrow\frac{144x}{x\left(x+2\right)}-\frac{100\left(x+2\right)}{x\left(x+2\right)}=\frac{2x\left(x+2\right)}{x\left(x+2\right)}\)
\(\Leftrightarrow144x-100\left(x+2\right)=2x\left(x+2\right)\Leftrightarrow144x-100x-200=2x^2+4x\)
\(\Leftrightarrow40x-200=2x^2\Leftrightarrow-2x^2+40x-200=0\)
\(\Leftrightarrow-2\left(x^2-20x+100\right)=0\Leftrightarrow-2\left(x-10\right)^2=0\)
\(\Leftrightarrow\left(x-10\right)^2=0\Leftrightarrow x=10\)
Vậy phương trình có tập nghiệm S = { 10 }
\(\Leftrightarrow\frac{144x-100x-200}{\left(x+2\right)x}-2=0\Leftrightarrow\frac{44x-200-2x^2-4x}{x^2+2x}=0\)
\(\Leftrightarrow40x-2x^2-200=0\Leftrightarrow20x-x^2-100=0\Leftrightarrow20x-x^2=100\)
\(\Leftrightarrow-\left(20x-x^2\right)=-100\Leftrightarrow x^2-20x=-100\Leftrightarrow x^2-20x+100=0\)
\(\Leftrightarrow\left(x-10\right)^2=0\Leftrightarrow x=10.\text{vậy: x=10}\)
