Question 621363
Since the denominators have no known common factors, the best you can do is use the product of the denominators as your least (known) common denominator.
(b-2)/a={{{(b-2)/a=(b-2)(b+1)/a/(b+1)}}}
4b/(b+1)={{{4b/(b+1)=4b*a/a/(b+1)=4ab/a/(b+1)}}}
 
NOTE:
Sometimes there are common factors in the denominators that are not obvious as the common {{{2a}}} shared between
{{{(b-2)/4a=(b-2)/(2*(2a))}}} and {{{(a+1)/(4ab+2a)=(a+1)/((2a)*(2b+1))}}} and in that case, you do not need to include the common factor that many times. For that example the best equivalent fractions would be
{{{(b-2)/4a=(b-2)/(2*(2a))=(b-2)(2b+1)/(2*(2a)(2b+1))}}} and
{{{(a+1)/(4ab+2a)=(a+1)/((2a)*(2b+1))=2*(a+1)/(2*(2a)*(2b+1))}}}