Question

Solve the following equation and verify your answer:

\[\frac{x + 3}{x - 3} + \frac{x + 2}{x - 2} = 2\]

Answer 1

\[\frac{x + 3}{x - 3} + \frac{x + 2}{x - 2} = 2\]

\[\text{ or }\frac{x + 3}{x - 3} = 2 - \frac{x + 2}{x - 2}\]

\[\text{ or }\frac{x + 3}{x - 3} = \frac{2x - 4 - x - 2}{x - 2}\]

\[\text{ or }\frac{x + 3}{x - 3} = \frac{x - 6}{x - 2}\]

\[\text{ or }x^2 - 2x + 3x - 6 = x^2 - 3x - 6x + 18 [\text{ After cross multiplication }]\]

\[\text{ or }x^2 - x^2 + x + 9x = 18 + 6\]

\[\text{ or }10x = 24\]

\[\text{ or }x = \frac{24}{10}\]

\[\text{ or }x = \frac{12}{5}\]

\[\text{ Thus, }x = \frac{12}{5}\text{ is the solution of the given equation .}\]

\[\text{ Check: }\]

\[\text{ Substituting }x = \frac{12}{5}\text{ in the given equation, we get: }\]

\[\text{ L . H . S .} = \frac{\frac{12}{5} + 3}{\frac{12}{5} - 3} + \frac{\frac{12}{5} + 2}{\frac{12}{5} - 2} = \frac{12 + 15}{12 - 15} + \frac{12 + 10}{12 - 10} = \frac{27}{- 3} + \frac{22}{2} = \frac{54 - 66}{- 6} = \frac{- 12}{- 6} = 2\]

\[\text{ R . H . S . }= 2\]

\[ \therefore\text{ L . H . S . = R . H . S . for }x = \frac{12}{5}\]