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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
21
x
x
2
−
11
x
+
24
+
1
=
x
2
+
10
x
+
24
x
2
−
11
x
+
24
.
\frac{ 21 x }{ x^2 - 11 x + 24 } + 1=\frac{ x^2 + 10 x + 24 }{ x^2 - 11 x + 24 }.
x
2
−
11
x
+
24
21
x
+
1
=
x
2
−
11
x
+
24
x
2
+
10
x
+
24
.
Hence, without using a calculator, solve the inequality
21
x
x
2
−
11
x
+
24
>
−
1
\frac{ 21 x }{ x^2 - 11 x + 24 } > -1
x
2
−
11
x
+
24
21
x
>
−
1
[5]
Answer
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