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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
7
x
+
5
x
2
−
6
x
−
7
+
1
=
x
2
+
x
−
2
x
2
−
6
x
−
7
.
\frac{ 7 x + 5 }{ x^2 - 6 x - 7 } + 1=\frac{ x^2 + x - 2 }{ x^2 - 6 x - 7 }.
x
2
−
6
x
−
7
7
x
+
5
+
1
=
x
2
−
6
x
−
7
x
2
+
x
−
2
.
Hence, without using a calculator, solve the inequality
7
x
+
5
x
2
−
6
x
−
7
>
−
1
\frac{ 7 x + 5 }{ x^2 - 6 x - 7 } > -1
x
2
−
6
x
−
7
7
x
+
5
>
−
1
[5]
Answer
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