Advanced Math: Simplify this... (a/b - c/d) / (1/b - 1/d)?

(a/b - c/d) / (1/b - 1/d)

Advanced Math: Simplify this... (a/b - c/d) / (1/b - 1/d)?
(a/b - c/d) / (1/b - 1/d) find common denominators and add


=[(ad-cb)/bd]/[(d-b)/bd] cancel out the bd


=(ad-cb)/(d-b)
Reply:Top: (ad-cb)/bd


Bottom: (d-b)/bd





Take the reciprocal of bottom into the top.


Cancel out the bd's


=(ad-cb)/(d-b)
Reply:Look at the top part first: a/b - c/d


To get a common denominator, multiply the left fraction by (d/d) and the fraction on the right by (b/b).


So you get: ad/bd - cb/bd


Both fractions now have the same denominator, so you can combine them to get: (ad - cb)/bd





Now look at the bottom part: 1/b - 1/d


Get the common denominator here too; multiply the left fraction by (d/d) and the right fraction by (b/b).


So you get: d/bd - b/bd


Both now have the same denominator, so combine the fractions: (d - b)/bd





So now you have (ad - cb)/bd divided by (d - b)/bd. Flip the second fraction to make it multiplication instead.





(ad - cb)/bd * bd/(d - b)





bd cancels from both fractions, and you end up with (ad - cb)/(d - b)
Reply:a/b-c/d: Take the least common multiple of the denominators which would be bd. Hence a/b-c/d=ad/bd-cb/bd=(ad-cb)/bd.


Similarly, 1/b-1/d


=(d-b)/bd.


So the given equation would be: ({ad-cb)/bd}/{(d-b)/bd}. Multiplying both numerator and denominator by bd/(d-b), the given equation would be:


{(ad-cb)/bd}*bd/{(d-b)}


=ad-cb/(d-b).