Question

Solve the following equation and verify your answer:

\[\frac{x + 2}{x + 5} = \frac{x}{x + 6}\]

Answer 1

\[\frac{x + 2}{x + 5} = \frac{x}{x + 6}\]

\[\text{ or }x^2 + 2x + 6x + 12 = x^2 + 5x [\text{ After cross multiplication }]\]

\[\text{ or }x^2 - x^2 + 8x - 5x = - 12\]

\[\text{ or }3x = - 12\]

\[\text{ or }x = \frac{- 12}{3}\]

\[\text{ or }x = - 4\]

\[\text{ Thus, }x = - 4 \text{ is the solution of given equation . }\]

\[\text{ Check: }\]

\[\text{ Substituting }x = - 4\text{ in the given equation, we get: }\]

\[\text{ L . H . S .} = \frac{- 4 + 2}{- 4 + 5} = - 2\]

\[\text{ R . H . S . }= \frac{- 4}{- 4 + 6} = - 2\]

\[ \therefore\text{ L . H . S . = R . H . S . for }x = - 4 .\]