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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
7
x
−
27
x
2
+
8
x
+
15
+
1
=
x
2
+
x
−
12
x
2
+
8
x
+
15
.
\frac{ - 7 x - 27 }{ x^2 + 8 x + 15 } + 1=\frac{ x^2 + x - 12 }{ x^2 + 8 x + 15 }.
x
2
+
8
x
+
15
−
7
x
−
27
+
1
=
x
2
+
8
x
+
15
x
2
+
x
−
12
.
Hence, without using a calculator, solve the inequality
−
7
x
−
27
x
2
+
8
x
+
15
>
−
1
\frac{ - 7 x - 27 }{ x^2 + 8 x + 15 } > -1
x
2
+
8
x
+
15
−
7
x
−
27
>
−
1
[5]
Answer
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