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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
2
x
2
−
23
x
+
27
x
2
+
6
x
−
7
+
3
=
x
2
−
5
x
+
6
x
2
+
6
x
−
7
.
\frac{ - 2 x^2 - 23 x + 27 }{ x^2 + 6 x - 7 } + 3=\frac{ x^2 - 5 x + 6 }{ x^2 + 6 x - 7 }.
x
2
+
6
x
−
7
−
2
x
2
−
23
x
+
27
+
3
=
x
2
+
6
x
−
7
x
2
−
5
x
+
6
.
Hence, without using a calculator, solve the inequality
−
2
x
2
−
23
x
+
27
x
2
+
6
x
−
7
>
−
3
\frac{ - 2 x^2 - 23 x + 27 }{ x^2 + 6 x - 7 } > -3
x
2
+
6
x
−
7
−
2
x
2
−
23
x
+
27
>
−
3
[5]
Answer
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