a) \(\dfrac{x+4}{x+5}:\dfrac{x+5}{x+6}:\dfrac{x+6}{x+4}\)
\(=\dfrac{x+4}{x+5}:\left(\dfrac{x+5}{x+6}\cdot\dfrac{x+6}{x+4}\right)\)
\(=\dfrac{x+4}{x+5}:\dfrac{x+5}{x+4}\)
\(=\dfrac{x+4}{x+5}\cdot\dfrac{x+4}{x+5}\)
\(=\left(\dfrac{x+4}{x+5}\right)^2\)
b) \(\dfrac{x-7}{x+8}:\left(\dfrac{x-7}{x-9}:\dfrac{x+8}{x-9}\right)\)
\(=\dfrac{x-7}{x+8}:\left(\dfrac{x-7}{x-9}\cdot\dfrac{x-9}{x+8}\right)\)
\(=\dfrac{x-7}{x+8}:\dfrac{x-7}{x+8}\)
\(=\dfrac{x-7}{x-8}\cdot\dfrac{x+8}{x-7}\)
\(=1\)
a: ĐKXĐ:\(x\notin\left\{-4;-5;-6\right\}\)
\(\dfrac{x+4}{x+5}:\dfrac{x+5}{x+6}:\dfrac{x+6}{x+4}\)
\(=\dfrac{x+4}{x+5}\cdot\dfrac{x+6}{x+5}\cdot\dfrac{x+4}{x+6}\)
\(=\dfrac{\left(x+4\right)^2}{\left(x+5\right)^2}\)
b: ĐKXĐ:\(x\notin\left\{7;-8;9\right\}\)
\(\dfrac{x-7}{x+8}:\left(\dfrac{x-7}{x-9}:\dfrac{x+8}{x-9}\right)\)
\(=\dfrac{x-7}{x+8}:\left(\dfrac{x-7}{x-9}\cdot\dfrac{x-9}{x+8}\right)\)
\(=\dfrac{x-7}{x+8}:\dfrac{x-7}{x+8}\)
=1
Lời giải:
a. \(\frac{x+4}{x+5}: \frac{x+5}{x+6}: \frac{x+6}{x+4}=\frac{x+4}{x+5}.\frac{x+6}{x+5}.\frac{x+4}{x+6}=\frac{1}{(x+5)^2}\)
b. \(\frac{x-7}{x+8}:(\frac{x-7}{x-9}: \frac{x+8}{x-9})=\frac{x-7}{x+8}:(\frac{x-7}{x-9}.\frac{x-9}{x+8})\\ =\frac{x-7}{x+8}:\frac{x-7}{x+8}=1\)
