Question

(10x+8/x)+18=10(8/x)+x

Answer 1

10x+8/x+18=80/x+x
by lcm
(10x^2+8+18x)/x=(80+x^2)/x
both side multiply by x and then x cancel
now 10x^2+8+18x=80+x^2
10x^2-x^2+18x+8-80=0
9x^2+18x-72=0
taking 9 common
then x^2+2x-8=0
now it is quardratic equation
x^2+4x-2x-8=0
x(x+4)-2(x+4)=0
now x+4=0 and x-2=o
now x=-4and x=2

Answer 2

10x+8/x + 18 = 10 (8/x) + x
10 x² + 8 + 18x/x = 80/x + x
10x²+8+ 18x = 80 + x²
9x²+18x - 72 =0
divide this equation by 9 
x²+ 2x - 8 = 0
use shri dhan achayra mathod to get the value of x

-b +,- √b²-4ac   ÷2a
-2+,- √2² - 4 × 1 × -8 / 2 ×1 
-2 + √4 + 32 ÷ 2
(-2 + √36) ÷ 2
(-2+6)÷2
x=2

now take negative 

(-2 - 6) / 2
x= -4