\(a,6:\left(2x+3\right)=15:\left(7x-3\right)\)
\(\Leftrightarrow\frac{6}{2x+3}=\frac{15}{7x-3}\)
\(\text{Áp dụng tính chất dãy tỉ số bằng nhau:}\)
\(\Leftrightarrow\frac{6}{2x+3}=\frac{15}{7x-3}=\frac{6+15}{2x+3+7x-3}=\frac{7}{3x}\)
\(\Leftrightarrow\frac{6}{2x+3}=\frac{7}{3x}\)
\(\Leftrightarrow6.3x=\left(2x+3\right).7\)
\(\Leftrightarrow18x=14x+21\)
\(\Leftrightarrow18x-14x=21\)
\(\Leftrightarrow4x=21\)
\(\Leftrightarrow x=21:4\)
\(\Leftrightarrow x=\frac{21}{4}\) \(\text{Vậy }x=\frac{21}{4}\)
\(b,\frac{11x-2}{7x+5}=\frac{11}{8}\)
\(\Leftrightarrow\frac{11x-2}{11}=\frac{7x+5}{8}\)
\(\text{Áp dụng tính chất dãy tỉ số bằng nhau:}\)
\(\Leftrightarrow\frac{11x-2}{11}=\frac{7x+5}{8}=\frac{11x-2-7x-5}{11-8}=\frac{4x-7}{3}\)
\(\Leftrightarrow\frac{11x-2}{11}=\frac{4x-7}{3}\)
\(\Leftrightarrow\left(11x-2\right).3=\left(4x-7\right).11\)
\(\Leftrightarrow33x-6=44x-77\)
\(\Leftrightarrow33x=44x-77+6\)
\(\Leftrightarrow33x=44x-71\)
\(\Leftrightarrow33x-44x=-71\)
\(\Leftrightarrow-11x=-71\)
\(\Leftrightarrow x=-71:\left(-11\right)\)
\(\Leftrightarrow x=\frac{71}{11}\) \(\text{Vậy }x=\frac{71}{11}\)
\(c,\frac{2x-1}{9}=\frac{-9}{1-2x}\)
\(\text{Áp dụng tính chất dãy tỉ số bằng nhau:}\)
\(\frac{2x-1}{9}=\frac{-9}{1-2x}=\frac{2x-1+9}{9-1-2x}=\frac{2x-8}{8-2x}\)
\(\Leftrightarrow\frac{2x-1}{9}=\frac{2x-8}{8-2x}\)
\(\Leftrightarrow\left(2x-1\right).\left(8-2x\right)=9.\left(2x-8\right)\)
\(\Leftrightarrow2x.\left(8-2x\right)-1.\left(8-2x\right)=18x-72\)
\(\Leftrightarrow16x-4x^2-8+2x=18x-72\)
\(\Leftrightarrow18x-4x^2-8-18x=-72\)
\(\Leftrightarrow-4x^2-8=-72\)
\(\Leftrightarrow-4x^2=-64\)
\(\Leftrightarrow x^2=16\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\left(\text{loại vì khi thử lại sai}\right)\\x=-4\end{matrix}\right.\)
\(\text{Vậy }x=-4\)
