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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
16
x
+
16
x
2
+
6
x
+
5
+
1
=
x
2
−
10
x
+
21
x
2
+
6
x
+
5
.
\frac{ - 16 x + 16 }{ x^2 + 6 x + 5 } + 1=\frac{ x^2 - 10 x + 21 }{ x^2 + 6 x + 5 }.
x
2
+
6
x
+
5
−
16
x
+
16
+
1
=
x
2
+
6
x
+
5
x
2
−
10
x
+
21
.
Hence, without using a calculator, solve the inequality
−
16
x
+
16
x
2
+
6
x
+
5
<
−
1
\frac{ - 16 x + 16 }{ x^2 + 6 x + 5 } < -1
x
2
+
6
x
+
5
−
16
x
+
16
<
−
1
[5]
Answer
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