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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
2
x
−
61
x
2
+
2
x
−
3
+
1
=
x
2
−
64
x
2
+
2
x
−
3
.
\frac{ - 2 x - 61 }{ x^2 + 2 x - 3 } + 1=\frac{ x^2 - 64 }{ x^2 + 2 x - 3 }.
x
2
+
2
x
−
3
−
2
x
−
61
+
1
=
x
2
+
2
x
−
3
x
2
−
64
.
Hence, without using a calculator, solve the inequality
−
2
x
−
61
x
2
+
2
x
−
3
>
−
1
\frac{ - 2 x - 61 }{ x^2 + 2 x - 3 } > -1
x
2
+
2
x
−
3
−
2
x
−
61
>
−
1
[5]
Answer
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