\(\frac{4}{2x+3}-\frac{7}{3x-5}=0\left(đkxđ:x\ne-\frac{3}{2};\frac{5}{3}\right)\)
\(< =>\frac{4\left(3x-5\right)}{\left(2x+3\right)\left(3x-5\right)}-\frac{7\left(2x+3\right)}{\left(2x+3\right)\left(3x-5\right)}=0\)
\(< =>12x-20-14x-21=0\)
\(< =>2x+41=0< =>x=-\frac{41}{2}\left(tm\right)\)
\(\frac{4}{2x-3}+\frac{4x}{4x^2-9}=\frac{1}{2x+3}\left(đk:x\ne-\frac{3}{2};\frac{3}{2}\right)\)
\(< =>\frac{4\left(2x+3\right)}{\left(2x-3\right)\left(2x+3\right)}+\frac{4x}{\left(2x-3\right)\left(2x+3\right)}-\frac{2x-3}{\left(2x+3\right)\left(2x-3\right)}=0\)
\(< =>8x+12+4x-2x+3=0\)
\(< =>10x=15< =>x=\frac{15}{10}=\frac{3}{2}\left(ktm\right)\)
\(\frac{2}{2x+1}+\frac{x}{4x^2-1}=\frac{7}{2x-1}\left(đkxđ:x\ne-\frac{1}{2};\frac{1}{2}\right)\)
\(< =>\frac{2\left(2x-1\right)}{\left(2x+1\right)\left(2x-1\right)}+\frac{x}{\left(2x+1\right)\left(2x-1\right)}=\frac{7\left(2x+1\right)}{\left(2x+1\right)\left(2x-1\right)}\)
\(< =>4x-2+x=14x+7\)
\(< =>14x-5x=-2-7\)
\(< =>9x=-9< =>x=-\frac{9}{9}=-1\left(tm\right)\)
\(\frac{x^2+5}{25-x^2}=\frac{3}{x+5}+\frac{x}{x-5}\left(đkxđ:x\ne-5;5\right)\)
\(< =>\frac{x^2+5}{\left(5-x\right)\left(5+x\right)}=\frac{3\left(5-x\right)}{\left(5+x\right)\left(5-x\right)}-\frac{x\left(x+5\right)}{\left(5+x\right)\left(5-x\right)}\)
\(< =>x^2+5=15-3x-x^2-5x\)\(< =>2x^2-8x-10=0\)
\(< =>2x^2+2x-10x-10=0\)
\(< =>2x\left(x+1\right)-10\left(x+1\right)=0\)
\(< =>\left(2x-10\right)\left(x+1\right)=0\)
\(< =>\orbr{\begin{cases}x=5\left(ktm\right)\\x=-1\left(tm\right)\end{cases}}\)
