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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
x
2
+
12
x
−
91
x
2
−
6
x
+
5
+
2
=
x
2
−
81
x
2
−
6
x
+
5
.
\frac{ - x^2 + 12 x - 91 }{ x^2 - 6 x + 5 } + 2=\frac{ x^2 - 81 }{ x^2 - 6 x + 5 }.
x
2
−
6
x
+
5
−
x
2
+
12
x
−
91
+
2
=
x
2
−
6
x
+
5
x
2
−
81
.
Hence, without using a calculator, solve the inequality
−
x
2
+
12
x
−
91
x
2
−
6
x
+
5
>
−
2
\frac{ - x^2 + 12 x - 91 }{ x^2 - 6 x + 5 } > -2
x
2
−
6
x
+
5
−
x
2
+
12
x
−
91
>
−
2
[5]
Answer
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