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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
2
x
2
−
4
x
+
14
x
2
+
5
x
+
6
−
1
=
x
2
−
9
x
+
8
x
2
+
5
x
+
6
.
\frac{ 2 x^2 - 4 x + 14 }{ x^2 + 5 x + 6 } - 1=\frac{ x^2 - 9 x + 8 }{ x^2 + 5 x + 6 }.
x
2
+
5
x
+
6
2
x
2
−
4
x
+
14
−
1
=
x
2
+
5
x
+
6
x
2
−
9
x
+
8
.
Hence, without using a calculator, solve the inequality
2
x
2
−
4
x
+
14
x
2
+
5
x
+
6
>
1
\frac{ 2 x^2 - 4 x + 14 }{ x^2 + 5 x + 6 } > 1
x
2
+
5
x
+
6
2
x
2
−
4
x
+
14
>
1
[5]
Answer
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