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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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3
x
2
+
10
x
+
23
x
2
−
x
−
2
−
2
=
x
2
+
12
x
+
27
x
2
−
x
−
2
.
\frac{ 3 x^2 + 10 x + 23 }{ x^2 - x - 2 } - 2=\frac{ x^2 + 12 x + 27 }{ x^2 - x - 2 }.
x
2
−
x
−
2
3
x
2
+
10
x
+
23
−
2
=
x
2
−
x
−
2
x
2
+
12
x
+
27
.
Hence, without using a calculator, solve the inequality
3
x
2
+
10
x
+
23
x
2
−
x
−
2
<
2
\frac{ 3 x^2 + 10 x + 23 }{ x^2 - x - 2 } < 2
x
2
−
x
−
2
3
x
2
+
10
x
+
23
<
2
[5]
Answer
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