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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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2
x
2
+
3
x
−
47
x
2
−
x
−
2
−
1
=
x
2
+
4
x
−
45
x
2
−
x
−
2
.
\frac{ 2 x^2 + 3 x - 47 }{ x^2 - x - 2 } - 1=\frac{ x^2 + 4 x - 45 }{ x^2 - x - 2 }.
x
2
−
x
−
2
2
x
2
+
3
x
−
47
−
1
=
x
2
−
x
−
2
x
2
+
4
x
−
45
.
Hence, without using a calculator, solve the inequality
2
x
2
+
3
x
−
47
x
2
−
x
−
2
<
1
\frac{ 2 x^2 + 3 x - 47 }{ x^2 - x - 2 } < 1
x
2
−
x
−
2
2
x
2
+
3
x
−
47
<
1
[5]
Answer
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