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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
2
x
2
+
22
x
+
50
x
2
+
9
x
+
14
−
1
=
x
2
+
13
x
+
36
x
2
+
9
x
+
14
.
\frac{ 2 x^2 + 22 x + 50 }{ x^2 + 9 x + 14 } - 1=\frac{ x^2 + 13 x + 36 }{ x^2 + 9 x + 14 }.
x
2
+
9
x
+
14
2
x
2
+
22
x
+
50
−
1
=
x
2
+
9
x
+
14
x
2
+
13
x
+
36
.
Hence, without using a calculator, solve the inequality
2
x
2
+
22
x
+
50
x
2
+
9
x
+
14
<
1
\frac{ 2 x^2 + 22 x + 50 }{ x^2 + 9 x + 14 } < 1
x
2
+
9
x
+
14
2
x
2
+
22
x
+
50
<
1
[5]
Answer
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