Solving Very Hard Algebra: Step by Step Guide

[Gringo123]

Well it's very hard for me anyway!
In both of the following expressions I have to make x the subject. Can anybody break them down for me and explain step by step how to solve them?

1.
ax/b + cx/d = e

2.
a/bx + c/d = e

From looking at the answers I know that the solutions are as follows:
1. x = edb/ad+bc
2. x = da/b(ed-c)

 

[Pythagorean]

Well it's very hard for me anyway!
In both of the following expressions I have to make x the subject. Can anybody break them down for me and explain step by step how to solve them?

1.
ax/b + cx/d = e

2.
a/bx + c/d = e

From looking at the answers I know that the solutions are as follows:
1. x = edb/ad+bc
2. x = da/b(ed-c)

I can give you a hint.

For 1. start by using the distributive property

 

[Gringo123]

So that would mean...
- ax/b + cx/d = e
- axd+cxb/bd = e
and from there I can get to the answer x = edb/ad+bc by using and rearranging the formula A=BC/D. Is that the right way to do it?

I've have tried applying the same logic to number and it doesn't seem to work.

Thanks for your help by the way.

 

[sylas]

So that would mean...
- ax/b + cx/d = e
- axd+cxb/bd = e
and from there I can get to the answer x = edb/ad+bc by using and rearranging the formula A=BC/D. Is that the right way to do it?

No; the above steps are incorrect. You've taken the term cx/d and multiplied top and bottom by b, which makes no difference to that term; but you've replaced ax/b with axd.

The distributive property, in this case, means you should look for a common factor. This is a good way to approach problem number 1. The original equation is
ax/b + cx/d = e

Can you see any common factors there?

Cheers -- sylas

PS. Your solution to number 1 needs some parentheses.