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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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−
x
2
−
23
x
+
84
x
2
+
6
x
−
27
+
2
=
x
2
−
11
x
+
30
x
2
+
6
x
−
27
.
\frac{ - x^2 - 23 x + 84 }{ x^2 + 6 x - 27 } + 2=\frac{ x^2 - 11 x + 30 }{ x^2 + 6 x - 27 }.
x
2
+
6
x
−
27
−
x
2
−
23
x
+
84
+
2
=
x
2
+
6
x
−
27
x
2
−
11
x
+
30
.
Hence, without using a calculator, solve the inequality
−
x
2
−
23
x
+
84
x
2
+
6
x
−
27
<
−
2
\frac{ - x^2 - 23 x + 84 }{ x^2 + 6 x - 27 } < -2
x
2
+
6
x
−
27
−
x
2
−
23
x
+
84
<
−
2
[5]
Answer
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