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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
13
x
+
6
x
2
+
5
x
+
6
+
1
=
x
2
−
8
x
+
12
x
2
+
5
x
+
6
.
\frac{ - 13 x + 6 }{ x^2 + 5 x + 6 } + 1=\frac{ x^2 - 8 x + 12 }{ x^2 + 5 x + 6 }.
x
2
+
5
x
+
6
−
13
x
+
6
+
1
=
x
2
+
5
x
+
6
x
2
−
8
x
+
12
.
Hence, without using a calculator, solve the inequality
−
13
x
+
6
x
2
+
5
x
+
6
<
−
1
\frac{ - 13 x + 6 }{ x^2 + 5 x + 6 } < -1
x
2
+
5
x
+
6
−
13
x
+
6
<
−
1
[5]
Answer
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