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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
9
x
+
9
x
2
+
5
x
−
14
+
1
=
x
2
−
4
x
−
5
x
2
+
5
x
−
14
.
\frac{ - 9 x + 9 }{ x^2 + 5 x - 14 } + 1=\frac{ x^2 - 4 x - 5 }{ x^2 + 5 x - 14 }.
x
2
+
5
x
−
14
−
9
x
+
9
+
1
=
x
2
+
5
x
−
14
x
2
−
4
x
−
5
.
Hence, without using a calculator, solve the inequality
−
9
x
+
9
x
2
+
5
x
−
14
>
−
1
\frac{ - 9 x + 9 }{ x^2 + 5 x - 14 } > -1
x
2
+
5
x
−
14
−
9
x
+
9
>
−
1
[5]
Answer
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