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

Question

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

Coudl you go into a little more detail. I know that's the correct answer but I don't understand how you derived it.

Answer 1

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)

Answer 2

properly i'm no longer going to do your homework for you, yet i'll inform you the regulations. a million. Any quantity raised to 0 is one, considering this can be an problem-free rule you will see both a) and b) are a million. 2. If 2 numbers have an same base and they are being expanded, you may in basic terms upload their exponents. ex. c) both have same base (c) so that you'll upload the exponents, ( 2+3=5). So the answer might want to be c^5 3. If 2 numbers have an same base and one is being divided by technique of the different, you may subtract their exponents. ex. If c) were: c^3 / c^2 , 3-2=a million, so the answer might want to be c^a million or in basic terms c 4. Any quantity raised to a adverse exponent equals its reciprocal with an excellent exponent i.e. b^-2 = (a million/b^2) and those are each of the regulations you want to end your homework. good success!

Answer 3

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).

Answer 4

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)

Answer 5

(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)