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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
7
x
−
9
x
2
+
2
x
−
15
+
1
=
x
2
−
5
x
−
24
x
2
+
2
x
−
15
.
\frac{ - 7 x - 9 }{ x^2 + 2 x - 15 } + 1=\frac{ x^2 - 5 x - 24 }{ x^2 + 2 x - 15 }.
x
2
+
2
x
−
15
−
7
x
−
9
+
1
=
x
2
+
2
x
−
15
x
2
−
5
x
−
24
.
Hence, without using a calculator, solve the inequality
−
7
x
−
9
x
2
+
2
x
−
15
>
−
1
\frac{ - 7 x - 9 }{ x^2 + 2 x - 15 } > -1
x
2
+
2
x
−
15
−
7
x
−
9
>
−
1
[5]
Answer
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