Porisma

A hint to get started

A rational identity and a scaled input

Show that 2x2+2x−8x2+x−6−1=x2+x−2x2+x−6\dfrac{2x^2+2x-8}{x^2+x-6}-1=\dfrac{x^2+x-2}{x^2+x-6}. mark

Hence, without using a calculator, solve the inequality 2x2+2x−8x2+x−6≤1\dfrac{2x^2+2x-8}{x^2+x-6}\leq1. marks

Deduce the solution to the inequality 4x2+2x−42x2+x−3≤1\dfrac{4x^2+2x-4}{2x^2+x-3}\leq1. marks

[2016/PJC/Promo/3]

CJC · Review Problems · Question 2

Move all terms to one side and identify zeros and forbidden denominator inputs before choosing intervals.

Read the worked solution