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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
8
x
2
+
8
x
+
15
+
1
=
x
2
+
8
x
+
7
x
2
+
8
x
+
15
.
\frac{ - 8 }{ x^2 + 8 x + 15 } + 1=\frac{ x^2 + 8 x + 7 }{ x^2 + 8 x + 15 }.
x
2
+
8
x
+
15
−
8
+
1
=
x
2
+
8
x
+
15
x
2
+
8
x
+
7
.
Hence, without using a calculator, solve the inequality
−
8
x
2
+
8
x
+
15
<
−
1
\frac{ - 8 }{ x^2 + 8 x + 15 } < -1
x
2
+
8
x
+
15
−
8
<
−
1
[5]
Answer
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