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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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−
2
x
2
+
8
x
−
54
x
2
−
4
x
+
3
+
3
=
x
2
−
4
x
−
45
x
2
−
4
x
+
3
.
\frac{ - 2 x^2 + 8 x - 54 }{ x^2 - 4 x + 3 } + 3=\frac{ x^2 - 4 x - 45 }{ x^2 - 4 x + 3 }.
x
2
−
4
x
+
3
−
2
x
2
+
8
x
−
54
+
3
=
x
2
−
4
x
+
3
x
2
−
4
x
−
45
.
Hence, without using a calculator, solve the inequality
−
2
x
2
+
8
x
−
54
x
2
−
4
x
+
3
>
−
3
\frac{ - 2 x^2 + 8 x - 54 }{ x^2 - 4 x + 3 } > -3
x
2
−
4
x
+
3
−
2
x
2
+
8
x
−
54
>
−
3
[5]
Answer
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