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\(\frac{x+7}{3}+\frac{x+5}{4}=\frac{x+3}{5}+\frac{x+1}{6}\)
\(\Rightarrow\frac{x+7}{3}+2+\frac{x+5}{4}+2=\frac{x+3}{5}+2+\frac{x+1}{6}+2\)
\(\Rightarrow\frac{x+13}{3}+\frac{x+13}{4}=\frac{x+13}{5}+\frac{x+13}{6}\)
\(\Rightarrow\frac{x+13}{3}+\frac{x+13}{4}-\frac{x+13}{5}-\frac{x+13}{6}=0\)
\(\Rightarrow\left(x+13\right)\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)=0\)
Vì \(\left(\frac{1}{3}>\frac{1}{4}>\frac{1}{5}>\frac{1}{6}\right)\Rightarrow\)\(\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)>0\)
\(\Rightarrow x+13=0\Leftrightarrow x=-13\)
\(\frac{x+m}{n+p}+\frac{x+n}{p+m}+\frac{x+p}{n+m}+3=0\)
\(\Rightarrow\frac{x+m}{n+p}+1+\frac{x+n}{p+m}+1+\frac{x+p}{n+m}+1=0\)
\(\Rightarrow\frac{x+m+n+p}{n+p}+\frac{x+m+n+p}{p+m}+\frac{x+m+n+p}{n+m}=0\)
\(\Rightarrow\left(x+m+n+p\right)\left(\frac{1}{n+p}+\frac{1}{p+m}+\frac{1}{n+m}\right)=0\)
Vì m,n,p là số dương nên \(\left(\frac{1}{n+p}+\frac{1}{p+m}+\frac{1}{n+m}\right)>0\)
\(\Rightarrow x+m+n+p=0\Rightarrow x=-\left(m+n+p\right)\)
\(\frac{5x+\frac{3x-4}{5}}{15}=\frac{\frac{3-x}{15}+7x}{5}+1-x\)
\(\Rightarrow\frac{\frac{25x+3x-4}{5}}{15}=\frac{\frac{3-x+105x}{15}}{5}+1-x\)
\(\Rightarrow\frac{\frac{28x-4}{5}}{15}=\frac{\frac{3+104x}{15}}{5}+1-x\)
\(\Rightarrow\frac{28x-4}{75}=\frac{3+104x}{75}+1-x\)
\(\Rightarrow\frac{28x-4}{75}=\frac{3+104x+75-75x}{75}\)
\(\Rightarrow\frac{28x-4}{75}=\frac{78+29x}{75}\)
\(\Rightarrow28x-4=78+29x\)
\(\Rightarrow x=-82\)
a,\(4x\left(2x+3\right)-x\left(8x-1\right)=5\left(x+2\right)\)
\(< =>8x^2+12x-8x^2+x=5x+10\)
\(< =>13x=5x+10< =>8x=10\)
\(< =>x=\frac{10}{8}=\frac{5}{4}\)
b, \(\left(3x-5\right)\left(3x+5\right)-x\left(9x-1\right)=4\)
\(< =>9x^2-25-9x^2+x=4\)
\(< =>x=4+29=33\)
c,\(3-4x\left(25-2x\right)=8x^2+x-300\)
\(< =>3-100x+8x^2=8x^2+x-300\)
\(< =>x+100x=3+300\)
\(< =>101x=303< =>x=\frac{303}{101}=3\)
d,\(2\left(1-\frac{3x}{5}\right)-\frac{2+3x}{10}=7-\frac{3\left(2x+1\right)}{4}\)
\(< =>2-\frac{6x}{5}-\frac{2+3x}{10}=7-\frac{6x+3}{4}\)
\(< =>-\frac{24x}{20}-\frac{4+6x}{20}+\frac{30x+15}{20}=5\)
\(< =>\frac{30x-6x-24x+15-4}{20}=5\)
\(< =>\frac{11}{5}=5< =>11=25\)(vo li)
