Why in these types of questions(the image) I need to multiply the dominator by itself and by the nominator. and why I can't just multiply it just by itself.

Yis the midpoint of xz. for each pair of points given, find the coordinates of the third point. 3. x( 5, 5), z(-1,5) 4. z( 2, 8), y(-2, 2) 7 points each xc find the indicated values. 5. b is between a and c. ab = 2x + 1, bc = 3x – 4, and ac = 62. find the value of 'x', and determine if b is a bisector. 7 points each x = bisector: yes or no? 6. m is between l and n. lm = 7x-1, mn = 2x + 4, and ln = 12. find the value of 'x' an determine if m is a bisector. x = bisector: yes or no?