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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
x
2
−
13
x
+
42
x
2
−
1
+
2
=
x
2
−
13
x
+
40
x
2
−
1
.
\frac{ - x^2 - 13 x + 42 }{ x^2 - 1 } + 2=\frac{ x^2 - 13 x + 40 }{ x^2 - 1 }.
x
2
−
1
−
x
2
−
13
x
+
42
+
2
=
x
2
−
1
x
2
−
13
x
+
40
.
Hence, without using a calculator, solve the inequality
−
x
2
−
13
x
+
42
x
2
−
1
<
−
2
\frac{ - x^2 - 13 x + 42 }{ x^2 - 1 } < -2
x
2
−
1
−
x
2
−
13
x
+
42
<
−
2
[5]
Answer
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