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Question 0107a
Equations and Inequalities
2007 Paper 1 Question 1 Variant
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Show that
−
2
x
2
−
10
x
2
+
x
−
6
+
3
=
x
2
+
3
x
−
28
x
2
+
x
−
6
.
\frac{ - 2 x^2 - 10 }{ x^2 + x - 6 } + 3=\frac{ x^2 + 3 x - 28 }{ x^2 + x - 6 }.
x
2
+
x
−
6
−
2
x
2
−
10
+
3
=
x
2
+
x
−
6
x
2
+
3
x
−
28
.
Hence, without using a calculator, solve the inequality
−
2
x
2
−
10
x
2
+
x
−
6
>
−
3
\frac{ - 2 x^2 - 10 }{ x^2 + x - 6 } > -3
x
2
+
x
−
6
−
2
x
2
−
10
>
−
3
[5]
Answer
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