\(\frac{144}{x-3}-\frac{144}{x}=4\)
\(144x-144\left(x-3\right)=4\)
\(144x-144x+144.3=4\)
\(144x-144x+432=4\)
\(432-4\)
=> Không tìm được x thỏa mãn
\(\frac{144}{x-3}-\frac{144}{x}=4\)
\(ĐKXĐ:x\ne3;x\ne0\)
\(\Leftrightarrow\frac{144x-144\left(x-3\right)}{x\left(x-3\right)}=4\)
\(\Leftrightarrow\frac{144x-144x+432}{x^2-3x}=4\)
\(\Leftrightarrow\frac{432}{x^2-3x}=4\)
\(\Leftrightarrow x^2-3x=\frac{432}{4}\)
\(\Leftrightarrow x^2-3x=108\)
\(\Leftrightarrow x^2-3x-108=0\)
\(\Leftrightarrow x^2+9x-12x-108=0\)
\(\Leftrightarrow\left(x^2+9x\right)-\left(12x+108\right)=0\)
\(\Leftrightarrow x\left(x+9\right)-12\left(x+9\right)=0\)
\(\Leftrightarrow\left(x+9\right)\left(x-12\right)=0\)
Hoặc \(x+9=0\Leftrightarrow x=-9\left(N\right)\)
Hoặc \(x-12=0\Leftrightarrow x=12\left(N\right)\)
Vậy tập nghiệm của phương trình là \(S=\left\{-9;12\right\}\)
\(\frac{114}{x-3}\)-\(\frac{144}{x}\)=4
144(\(\frac{1}{x-3}\)-\(\frac{1}{x}\))=4
\(\frac{x}{\left(x-3\right)x}\)-\(\frac{x-3}{x\left(x-3\right)}\)=4:144=\(\frac{1}{36}\)
\(\frac{x-\left(x-3\right)}{x\left(x-3\right)}\)=\(\frac{1}{36}\)
\(\frac{x-x+3}{x\left(x-3\right)}\)=\(\frac{1}{36}\)
\(\frac{3}{x\left(x-3\right)}\)=\(\frac{1}{36}\)
=>x(x-30)=36.3=108=12.9
=>x=12
