Question 0107a

Equations and Inequalities
2007 Paper 1 Question 1 Variant

Question

Show that
2x2+22x+50x2+9x+141=x2+13x+36x2+9x+14.\frac{ 2 x^2 + 22 x + 50 }{ x^2 + 9 x + 14 } - 1=\frac{ x^2 + 13 x + 36 }{ x^2 + 9 x + 14 }.
Hence, without using a calculator, solve the inequality
2x2+22x+50x2+9x+14<1\frac{ 2 x^2 + 22 x + 50 }{ x^2 + 9 x + 14 } < 1
[5]

Answer