Question

Question #3127e

Answer 1

`b = (cd -ac)/(a-d-ac)`

Explanation:

The problem is that there is more than one term with `b`.

Remove the brackets:

`a(b+c) -d(b+c) = abc`

`color(blue)(ab) + ac color(blue)(-bd) -cd = color(blue)(abc)" "larr`move all 'b' terms to one side

`color(blue)(ab -bd -abc) = -ac +cd" "larr` Factor out 'b'

`color(red)(b)(a-d -ac) = -ac +cd" "larr` there is now only one 'b'

`color(red)(b) = (cd -ac)/(a-d-ac)" "larr` divide to isolate 'b'