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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
4
x
+
2
x
2
+
x
−
12
+
1
=
x
2
−
3
x
−
10
x
2
+
x
−
12
.
\frac{ - 4 x + 2 }{ x^2 + x - 12 } + 1=\frac{ x^2 - 3 x - 10 }{ x^2 + x - 12 }.
x
2
+
x
−
12
−
4
x
+
2
+
1
=
x
2
+
x
−
12
x
2
−
3
x
−
10
.
Hence, without using a calculator, solve the inequality
−
4
x
+
2
x
2
+
x
−
12
<
−
1
\frac{ - 4 x + 2 }{ x^2 + x - 12 } < -1
x
2
+
x
−
12
−
4
x
+
2
<
−
1
[5]
Answer
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