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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
4
x
2
+
38
x
+
82
x
2
+
9
x
+
18
−
3
=
x
2
+
11
x
+
28
x
2
+
9
x
+
18
.
\frac{ 4 x^2 + 38 x + 82 }{ x^2 + 9 x + 18 } - 3=\frac{ x^2 + 11 x + 28 }{ x^2 + 9 x + 18 }.
x
2
+
9
x
+
18
4
x
2
+
38
x
+
82
−
3
=
x
2
+
9
x
+
18
x
2
+
11
x
+
28
.
Hence, without using a calculator, solve the inequality
4
x
2
+
38
x
+
82
x
2
+
9
x
+
18
<
3
\frac{ 4 x^2 + 38 x + 82 }{ x^2 + 9 x + 18 } < 3
x
2
+
9
x
+
18
4
x
2
+
38
x
+
82
<
3
[5]
Answer
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