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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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3
x
2
+
21
x
+
4
x
2
+
6
x
−
7
−
2
=
x
2
+
9
x
+
18
x
2
+
6
x
−
7
.
\frac{ 3 x^2 + 21 x + 4 }{ x^2 + 6 x - 7 } - 2=\frac{ x^2 + 9 x + 18 }{ x^2 + 6 x - 7 }.
x
2
+
6
x
−
7
3
x
2
+
21
x
+
4
−
2
=
x
2
+
6
x
−
7
x
2
+
9
x
+
18
.
Hence, without using a calculator, solve the inequality
3
x
2
+
21
x
+
4
x
2
+
6
x
−
7
>
2
\frac{ 3 x^2 + 21 x + 4 }{ x^2 + 6 x - 7 } > 2
x
2
+
6
x
−
7
3
x
2
+
21
x
+
4
>
2
[5]
Answer
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