5/x-2 - 4/x-3 express as a single fraction in its simplest form. I had done the question like this: = 5/x-2 (x-2)(x-3) -4/x-3 (x-2)(x-3) = 5x-15-4x+8 = x-7 but how in fraction?

Question

5/x-2 - 4/x-3 express as a single fraction in its simplest form.          I had done the question like this:      =   5/x-2 (x-2)(x-3) -4/x-3 (x-2)(x-3) =   5x-15-4x+8                         =   x-7                                 but how in fraction?

Reiny · Answer

just like in 5/6 - 3/7 you will need a common denominator.
In my example, it would be 42?
How did I get 42 ?
Next step
35/42 - 18/42 ---> how did I get those fractions
= 17/42

Now to your problem
5/(x-2) - 4(x-3)
LCD = (x-2)(x-3) ---> same step as above e.g
= 5(x-3)/((x-2)(x-3)) - 4(x-2)/((x-2)(x-3))
= (5x-15 -4x+8)/((x-2)(x-3))
= (x - 7)/((x-2)(x-3))