Question

Thực hiện phép tính

\(\left(\frac{x+3}{x-3}-\frac{x-3}{x+3}\right)\cdot\left(\frac{1}{3}+\frac{1}{x}\right)\)

Answer 1

$(\backslash (\backslash frac\{x+3\}\{x-3\}\backslash )\; -\; \backslash (\backslash frac\{x-3\}\{x+3\}\backslash ))\; .\; (\backslash (\backslash frac\{1\}\{3\}\backslash )\; +\; \backslash (\backslash frac\{1\}\{x\}\backslash ))$

= [\(\frac{\left(x+3\right)^2-\left(x-3\right)^2}{\left(x-3\right)\left(x+3\right)}\)] . \(\frac{x+3}{3x}\)

= \(\frac{\left(x+3\right)^2-\left(x-3\right)^2}{\left(x-3\right).3x}\)

= \(\frac{x^2+6x+9-x^2+6x-9}{\left(x-3\right).3x}\)

=\(\frac{12x}{\left(x-3\right).3x}\)

= \(\frac{4}{x-3}\)