Edexcel A-Level Mathematics A2 Fp2 1 1 Manipulation and Solution Questions

Practise Edexcel IAL FP2.1.1 by splitting modulus cases, solving rational inequalities at critical values and stating intervals that exclude undefined denominators.

Exam points

split a modulus inequality into positive and negative cases, then combine the valid x intervals
solve rational inequalities by finding denominator and numerator critical values and testing intervals
state excluded denominator values explicitly when reporting the solution set

[Maximum number: 6]

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

Use algebra to determine the values of x for which

\frac{x+1}{(x-3)(x+2)}\le 1-\frac{2}{x-3}

Critical values from the denominator are x=-2 and x=3.

Equating the two sides:

\frac{x+1}{(x-3)(x+2)}=1-\frac{2}{x-3}

x+1=x^2-x-6-2(x+2)

x^2-4x-11=0.

x=\frac{4\pm\sqrt{16+44}}{2}=2\pm\sqrt{15}

Therefore

x<-2,\qquad 2-\sqrt{15}\le x<3,\qquad x\ge 2+\sqrt{15}

All question bank results loaded

Edexcel A-Level Mathematics A2 Fp2 1 1 Manipulation and Solution Questions question 1