How can I solve and simplify these equations?

Question

Could someone please give step by step working on how to do these?

Solve:
14/x = 5/3(x-18.5)

Along with

Simplify:
(x+2)/x - (x-4)/x^2


Thanks!

Answer 1

Solve : 14 / x = 5 / [ 3(x - 18.5) ]
I think that's what it should be.

Cross-multiply to get rid of fractions :
14 * 3(x - 18.5) = 5 * x

Multiply out the LHS :
42x - 777 = 5x

Subtract 5x from both sides :
37x - 777 = 0

Add 777 to both sides :
37x = 777

Divide both sides by 37 :
x = 21
------------------------------------------
Simplify : (x + 2) / x - (x - 4) / x^2

The LCM of the denominators is x^2.

For the left-hand term, divide the x into the
LCM to get x, and then multiply this by (x + 2).
This results in x(x + 2).

For the right-hand term, divide the x^2 into the
LCM to get 1, and then multiply this by (x - 4).
This results in 1(x - 4), or just (x - 4).

Put them together to get :
[ x(x + 2) - (x - 4) ] / x^2

Multiply out the numerator :
(x^2 + 2x - x + 4) / x^2

Add up like terms :
(x^2 + x + 4) / x^2

This is the final simplified form.

Answer 2

14/x = 5/3(x-18.5)

multiply both by x

14 = 5x^2/3 - 18.5x/3 ==> rearrange

5/3x^2 - 18.5/3 x - 14 = 0 ==> easy stuff from here

x=32.65
x=-43.75

second one, simplify

(x+2)/x - (x-4)/x^2

1/x as a common factor so

1/x [ x+2 - (x-4)/x ] ==> develop (x-4)/x
1/x ( x+2 - x/x +4/x )
1/x ( x + 2 - 1 + 4/x )
1/x ( x +1 + 4/x)
(x+1)/x + 4

Answer 3

solve
14/x=5/3x-185/60
14+185/60=5/3x.x
.........no idea sorry i am only 8th grade but if you have the answer i would love to except it