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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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2
x
2
−
8
x
−
30
x
2
−
7
x
+
12
−
1
=
x
2
−
x
−
42
x
2
−
7
x
+
12
.
\frac{ 2 x^2 - 8 x - 30 }{ x^2 - 7 x + 12 } - 1=\frac{ x^2 - x - 42 }{ x^2 - 7 x + 12 }.
x
2
−
7
x
+
12
2
x
2
−
8
x
−
30
−
1
=
x
2
−
7
x
+
12
x
2
−
x
−
42
.
Hence, without using a calculator, solve the inequality
2
x
2
−
8
x
−
30
x
2
−
7
x
+
12
>
1
\frac{ 2 x^2 - 8 x - 30 }{ x^2 - 7 x + 12 } > 1
x
2
−
7
x
+
12
2
x
2
−
8
x
−
30
>
1
[5]
Answer
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