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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
2
x
2
+
6
x
2
−
8
x
−
9
−
1
=
x
2
+
8
x
+
15
x
2
−
8
x
−
9
.
\frac{ 2 x^2 + 6 }{ x^2 - 8 x - 9 } - 1=\frac{ x^2 + 8 x + 15 }{ x^2 - 8 x - 9 }.
x
2
−
8
x
−
9
2
x
2
+
6
−
1
=
x
2
−
8
x
−
9
x
2
+
8
x
+
15
.
Hence, without using a calculator, solve the inequality
2
x
2
+
6
x
2
−
8
x
−
9
<
1
\frac{ 2 x^2 + 6 }{ x^2 - 8 x - 9 } < 1
x
2
−
8
x
−
9
2
x
2
+
6
<
1
[5]
Answer
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