It’s not correct.
1/2 + 1/7 = 9/14
1 x 7 / 2 x 7 + 1 x 2 / 7 x2
= =
7/14 + 2/14
7 + 2 = 9 so it’s 9/14
Don’t need to change the denominators now that they are the same.
Your friend didn’t change it so that the denominators were the same on each fraction and multiplied the two numerators and denominators before changing it that’s where they made the mistake.