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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
3
x
2
+
9
x
+
2
x
2
−
9
−
2
=
x
2
+
9
x
+
20
x
2
−
9
.
\frac{ 3 x^2 + 9 x + 2 }{ x^2 - 9 } - 2=\frac{ x^2 + 9 x + 20 }{ x^2 - 9 }.
x
2
−
9
3
x
2
+
9
x
+
2
−
2
=
x
2
−
9
x
2
+
9
x
+
20
.
Hence, without using a calculator, solve the inequality
3
x
2
+
9
x
+
2
x
2
−
9
>
2
\frac{ 3 x^2 + 9 x + 2 }{ x^2 - 9 } > 2
x
2
−
9
3
x
2
+
9
x
+
2
>
2
[5]
Answer
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