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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
3
x
2
+
19
x
+
14
x
2
+
9
x
+
8
−
2
=
x
2
+
x
−
2
x
2
+
9
x
+
8
.
\frac{ 3 x^2 + 19 x + 14 }{ x^2 + 9 x + 8 } - 2=\frac{ x^2 + x - 2 }{ x^2 + 9 x + 8 }.
x
2
+
9
x
+
8
3
x
2
+
19
x
+
14
−
2
=
x
2
+
9
x
+
8
x
2
+
x
−
2
.
Hence, without using a calculator, solve the inequality
3
x
2
+
19
x
+
14
x
2
+
9
x
+
8
<
2
\frac{ 3 x^2 + 19 x + 14 }{ x^2 + 9 x + 8 } < 2
x
2
+
9
x
+
8
3
x
2
+
19
x
+
14
<
2
[5]
Answer
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