Question

Find a positive value of x for which the given equation is satisfied:

\[\frac{x^2 - 9}{5 + x^2} = - \frac{5}{9}\]

Answer 1

\[\frac{x^2 - 9}{5 + x^2} = \frac{- 5}{9}\]
\[\text{ or }9 x^2 - 81 = - 25 - 5 x^2 [\text{ After cross multiplication }]\]
\[\text{ or }9 x^2 + 5 x^2 = - 25 + 81\]
\[\text{ or }14 x^2 = 56\]
\[\text{ or }x^2 = \frac{56}{14}\]
\[\text{ or }x^2 = 4 = 2^2 \]
\[\text{ or }x = 2\]
\[\text{ Thus, }x = 2\text{ is the solution of the given equation . }\]
\[\text{ Check: }\]
\[\text{ Substituting }x = 2\text{ in the given equation, we get: }\]
\[\text{ L . H . S . }= \frac{2^2 - 9}{5 + 2^2} = \frac{4 - 9}{5 + 4} = \frac{- 5}{9}\]
\[\text{ R . H . S . }= \frac{- 5}{9}\]
\[ \therefore\text{ L . H . S . = R . H . S . for }x = 2 . \]