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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
16
x
+
34
x
2
+
3
x
+
2
+
1
=
x
2
−
13
x
+
36
x
2
+
3
x
+
2
.
\frac{ - 16 x + 34 }{ x^2 + 3 x + 2 } + 1=\frac{ x^2 - 13 x + 36 }{ x^2 + 3 x + 2 }.
x
2
+
3
x
+
2
−
16
x
+
34
+
1
=
x
2
+
3
x
+
2
x
2
−
13
x
+
36
.
Hence, without using a calculator, solve the inequality
−
16
x
+
34
x
2
+
3
x
+
2
>
−
1
\frac{ - 16 x + 34 }{ x^2 + 3 x + 2 } > -1
x
2
+
3
x
+
2
−
16
x
+
34
>
−
1
[5]
Answer
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