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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
4
x
2
+
34
x
+
57
x
2
+
8
x
+
12
−
3
=
x
2
+
10
x
+
21
x
2
+
8
x
+
12
.
\frac{ 4 x^2 + 34 x + 57 }{ x^2 + 8 x + 12 } - 3=\frac{ x^2 + 10 x + 21 }{ x^2 + 8 x + 12 }.
x
2
+
8
x
+
12
4
x
2
+
34
x
+
57
−
3
=
x
2
+
8
x
+
12
x
2
+
10
x
+
21
.
Hence, without using a calculator, solve the inequality
4
x
2
+
34
x
+
57
x
2
+
8
x
+
12
<
3
\frac{ 4 x^2 + 34 x + 57 }{ x^2 + 8 x + 12 } < 3
x
2
+
8
x
+
12
4
x
2
+
34
x
+
57
<
3
[5]
Answer
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