Question

find the reciprocal of -7/6+23/5​

Answer 1

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