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x = 1 or x = -2

Step-by-step explanation:

The first step is to find the L.C.M of the L.H.S

=

⇒ =

=

cross multiplying , we have

(x+5)(14x - 26) = 18(2x-5)

Expanding, we have

+ 44x - 130 = 36x - 90

+ 44x - 130 - 36x + 90 = 0

+ 8x - 40 = 0

solving the resulting quadratic equation by factorization , we have

(14x - 20)(x + 2 ) = 0

14x - 20 = 0  or x + 2 = 0

14x = 20       or x = -2

x = 20/ 14      or x = -2

Therefore x = 10/7 or x = -2

x = 1 or x = -2