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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
5
x
−
31
x
2
−
5
x
+
6
+
1
=
x
2
−
25
x
2
−
5
x
+
6
.
\frac{ 5 x - 31 }{ x^2 - 5 x + 6 } + 1=\frac{ x^2 - 25 }{ x^2 - 5 x + 6 }.
x
2
−
5
x
+
6
5
x
−
31
+
1
=
x
2
−
5
x
+
6
x
2
−
25
.
Hence, without using a calculator, solve the inequality
5
x
−
31
x
2
−
5
x
+
6
>
−
1
\frac{ 5 x - 31 }{ x^2 - 5 x + 6 } > -1
x
2
−
5
x
+
6
5
x
−
31
>
−
1
[5]
Answer
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