Without using a calculator, solve the inequality \(\frac{x^2 - 5x + 6}{x^2 - 4}

Question

Without using a calculator, solve the inequality $\frac{x^2 - 5x + 6}{x^2 - 4} < \frac{2x - 3}{x + 2}$.[4] Sketch on the same diagram the graphs of $y = \ln x$ and $y = x - 5$, giving the equations of any asymptotes and the $x$-coordinates of the points of intersection between the two graphs.[2] Hence solve the inequality $\ln |x| < |x| - 5$.[2]

Accepted Answer

(a)x 2 (b)(ii)x 6.94 and x$ eq$0

2025 RI P2 Q1

2025 RI P2 Q1