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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
7
x
−
33
x
2
+
4
x
−
21
+
1
=
x
2
−
3
x
−
54
x
2
+
4
x
−
21
.
\frac{ - 7 x - 33 }{ x^2 + 4 x - 21 } + 1=\frac{ x^2 - 3 x - 54 }{ x^2 + 4 x - 21 }.
x
2
+
4
x
−
21
−
7
x
−
33
+
1
=
x
2
+
4
x
−
21
x
2
−
3
x
−
54
.
Hence, without using a calculator, solve the inequality
−
7
x
−
33
x
2
+
4
x
−
21
>
−
1
\frac{ - 7 x - 33 }{ x^2 + 4 x - 21 } > -1
x
2
+
4
x
−
21
−
7
x
−
33
>
−
1
[5]
Answer
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