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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
2
x
−
34
x
2
+
x
−
6
+
1
=
x
2
+
3
x
−
40
x
2
+
x
−
6
.
\frac{ 2 x - 34 }{ x^2 + x - 6 } + 1=\frac{ x^2 + 3 x - 40 }{ x^2 + x - 6 }.
x
2
+
x
−
6
2
x
−
34
+
1
=
x
2
+
x
−
6
x
2
+
3
x
−
40
.
Hence, without using a calculator, solve the inequality
2
x
−
34
x
2
+
x
−
6
<
−
1
\frac{ 2 x - 34 }{ x^2 + x - 6 } < -1
x
2
+
x
−
6
2
x
−
34
<
−
1
[5]
Answer
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