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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
13
x
+
17
x
2
+
4
x
+
3
+
1
=
x
2
−
9
x
+
20
x
2
+
4
x
+
3
.
\frac{ - 13 x + 17 }{ x^2 + 4 x + 3 } + 1=\frac{ x^2 - 9 x + 20 }{ x^2 + 4 x + 3 }.
x
2
+
4
x
+
3
−
13
x
+
17
+
1
=
x
2
+
4
x
+
3
x
2
−
9
x
+
20
.
Hence, without using a calculator, solve the inequality
−
13
x
+
17
x
2
+
4
x
+
3
<
−
1
\frac{ - 13 x + 17 }{ x^2 + 4 x + 3 } < -1
x
2
+
4
x
+
3
−
13
x
+
17
<
−
1
[5]
Answer
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