What is the least common denominator of these? 1/4 9/2x 5/2(x+1)

The way you have written the expressions, only the numbers 2 and 4 appear in denominators. Their least common multiple is 4. Then your terms become
.. 1/4, (18/4)x (10/4)(x +1)

If you intend your expressions to be
.. 1/4, 9/(2x), 5/(2(x+1))
then the least common multiple of the denominators is 4*x*(x+1), and your expressions can be written as
.. x(x+1)/(4x(x+1))
.. 18(x+1)/(4x(x+1))
.. 10x/(4(x(x+1))


If you write a fraction using plain text, parentheses are required around any numerator containing a sum and around any denominator containing any arithmetic operation. It's all about order of operations. The division symbol only applies to the immediately preceding and the immediately following operand:
.. a+b/cd = a+(b/c)*d
If you want something else, use parentheses.
.. (a+b)/(cd) . . . . for example