Put under common denominator :
Expand all this stuff :
Expand further :
Cancel out terms :
Factorize both polynomials :
Cancel out :
I think it's right, I haven't checked though ...
When adding/substracting fractions, all fractions need to be under the same denominator, otherwise it won't work. To achieve this, we usually multiply both parts of fraction 1 by the denominator of fraction 2, and the other way round. Then, we substract (in your case) the fractions. (we are not substracting the denominators, obviously)
EDIT : did you see that ? 77 posts, and 7 thanks ... it's my lucky day ...
In the original fractions, the denominators are 2x-3 and . The least common denominator is . We need to multiply numerator and denominator of the first fraction, by x to get . Since the denominator of the second fraction is already x(2x-3), we don't have to change that.
You can, of course, multiply that denominator out to get .
Ah yes, I didn't think of that.
Surely because when I was in junior I used to multiply the two denominators (typically 7 and 9) together to be sure to get a common divisor, because I wouldn't want to think about it.
I must think of doing this little check ... thanks HallsofIvy