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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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3
x
2
−
x
−
54
x
2
+
3
x
−
18
−
2
=
x
2
−
7
x
−
18
x
2
+
3
x
−
18
.
\frac{ 3 x^2 - x - 54 }{ x^2 + 3 x - 18 } - 2=\frac{ x^2 - 7 x - 18 }{ x^2 + 3 x - 18 }.
x
2
+
3
x
−
18
3
x
2
−
x
−
54
−
2
=
x
2
+
3
x
−
18
x
2
−
7
x
−
18
.
Hence, without using a calculator, solve the inequality
3
x
2
−
x
−
54
x
2
+
3
x
−
18
>
2
\frac{ 3 x^2 - x - 54 }{ x^2 + 3 x - 18 } > 2
x
2
+
3
x
−
18
3
x
2
−
x
−
54
>
2
[5]
Answer
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