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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
2
x
2
+
12
x
−
19
x
2
−
6
x
+
8
+
3
=
x
2
−
6
x
+
5
x
2
−
6
x
+
8
.
\frac{ - 2 x^2 + 12 x - 19 }{ x^2 - 6 x + 8 } + 3=\frac{ x^2 - 6 x + 5 }{ x^2 - 6 x + 8 }.
x
2
−
6
x
+
8
−
2
x
2
+
12
x
−
19
+
3
=
x
2
−
6
x
+
8
x
2
−
6
x
+
5
.
Hence, without using a calculator, solve the inequality
−
2
x
2
+
12
x
−
19
x
2
−
6
x
+
8
<
−
3
\frac{ - 2 x^2 + 12 x - 19 }{ x^2 - 6 x + 8 } < -3
x
2
−
6
x
+
8
−
2
x
2
+
12
x
−
19
<
−
3
[5]
Answer
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