Question

Solve the following equation and verify your answer:

\[\frac{(x + 2)(2x - 3) - 2 x^2 + 6}{x - 5} = 2\]

Answer 1

\[\frac{(x + 2)(2x - 3) - 2 x^2 + 6}{x - 5} = 2\]

\[\text{ or }\frac{2 x^2 + x - 6 - 2 x^2 + 6}{x - 5} = 2\]

\[\text{ or }\frac{x}{x - 5} = 2\]

\[\text{ or }2x - 10 = x [\text{ After cross multiplication }]\]

\[\text{ or }2x - x = 10\]

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

\[\text{ Thus, }x = 10\text{ is the solution of the given equation . }\]

\[\text{ Check: }\]

\[\text{ Substituting }x = 10 \text{in the given equation, we get: } \]

\[\text{ L . H . S . }= \frac{(10 + 2)(2 \times 10 - 3) - 2 \times {10}^2 + 6}{10 - 5} = \frac{12 \times 17 - 200 + 6}{5} = \frac{10}{5} = 2\]

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

\[ \therefore \text{ L . H . S . = R . H . S . for }x = 10.\]