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