Algebraic Equation help

Show that;      7+   10  =  9
             -----    --
    x+2    x

Becomes; 7x^2 + 15x - 18 = 0
When I publish these cards, the x+2 is supposed to be under 10 and the x is supposed to under the 9, I hope it makes sense  

First step;

Imagine the 7 has a one under it.

Find the lowest common multiple first;

So we do (x+2) X (x)= x(x+2)

Then you would times 7 by x+2 (because I timsed the one by x+2 when I was finding a LCM) 

Then times the 10 by 1.

Second steps;

Our equation now looks like this;

7(x+2) + 10 = 9
--------------    ---
  (x+2)        x

Next you would expand the 7(x+2) so it becomes 7x+14, then add on the 10 so our equation is 7x+24.

Our full equation looks like this;

(7x+24)= 9
---------   ---
x+2        x

Third steps;

This is our equation;

(7x+24) = 9
----------  ---
x+2         x

Now we take the x and the x+2 on the opposite side so our new equation looks like this;

x(7x+24) = 9(x+2)

Fourth step;

Our equation is this;

x(7x+24) = 9(x+2)

Now we expand the brackets;

7x^2 + 24x = 9x + 18

Fifth step;

Our equation is this;

7x^2 + 24x = 9x + 18

Now we take everything onto the side which has the x^2.

We do 24x - 9x = 15x ( remember that when we take things over to the other side they change from + to -)

And we take the 18 to the other side.

Our new equation is this;

7x^2 + 15x - 18 = 0

I hope this makes sense, sorry about the first card, I didn't know how to fix it, but it seemed to type properly for the other cards :)