a) \(\dfrac{x}{x+1}=\dfrac{x+5}{x+7}\)
\(\Leftrightarrow x\left(x+7\right)=\left(x+1\right)\left(x+5\right)\)
\(\Leftrightarrow x^2+7x=\left(x+1\right)x+\left(x+1\right).5\)
\(\Leftrightarrow x^2+7x=x^2+x+5x+5\)
\(\Leftrightarrow x^2+7x=x^2+6x+5\)
\(\Leftrightarrow x^2+7x-6x-x^2=5\)
\(\Leftrightarrow x=5\)
Vậy...
b) \(\dfrac{x+7}{x+4}=\dfrac{x-1}{x-2}\)
\(\Leftrightarrow\left(x+7\right)\left(x-2\right)=\left(x+4\right)\left(x-1\right)\)
\(\Leftrightarrow\left(x+7\right)x-\left(x+7\right).2=\left(x+4\right)x-\left(x+4\right)\)
\(\Leftrightarrow x^2+7x-2x+14=x^2+4x-x-4\)
\(\Leftrightarrow x^2+5x+14=x^2+3x-4\)
\(\Leftrightarrow x^2+5x+14-3x-x^2=-4\)
\(\Leftrightarrow2x+14=-4\)
\(\Leftrightarrow2x=-18\)
\(\Leftrightarrow x=-9\)
Vậy...
c) \(\dfrac{x+2}{x-2}=\dfrac{x-3}{x+3}\)
\(\Leftrightarrow\left(x+2\right)\left(x+3\right)=\left(x-2\right)\left(x-3\right)\)
\(\Leftrightarrow\left(x+2\right)x+\left(x+2\right).3=\left(x-2\right)x-\left(x-2\right).3\)
\(\Leftrightarrow x^2+2x+3x+6=x^2-2x-3x+6\)
\(\Leftrightarrow x^2+5x+6=x^2-5x+6\)
\(\Leftrightarrow x^2+5x+6-6+5x-x^2=0\)
\(\Leftrightarrow10x=0\)
\(\Leftrightarrow x=0\)
Vậy...
