find the reciprocal of -7/6+23/5
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Let x be the number.
We are told that the number subtracted from twice its reciprocal is equal to
−
23
5
Hence:
2
x
−
x
=
−
23
5
Multiply through by x and cross multiply
→
5
(
2
−
x
2
)
=
−
23
x
Expand
→
10
−
5
x
2
=
−
23
x
−
5
x
2
+
23
x
+
10
=
0
5
x
2
−
23
x
−
10
=
0
Factorise
→
(
x
−
5
)
(
5
x
+
2
)
=
0
Hence x = either 5 or
−
2
5
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