1. ## Algebraic Ratio

Hey, could someone please solve this (go through each step if possible):

=(a/b-c/b)*(a-b/2(a/b-c/b))

The answer is apparently, (a^2/2b)-(c^2/2b), but I cant work it out

Thanks

2. ## Re: Algebraic Ratio

Originally Posted by Albatrossie
Hey, could someone please solve this (go through each step if possible):
=(a/b-c/b)*(a-b/2(a/b-c/b))
The answer is apparently, (a^2/2b)-(c^2/2b), but I cant work it out
That answer is correct; better shown as: (a^2 - c^2) / (2b)

Your expression is somewhat ambiguous (even if correctly shown); this is clearer:
(a/b - c/b) * [a - b(a/b - c/b) / 2]

Try this way:
x = (a/b - c/b) ; so expression becomes:

x * [(a - bx) / 2]

Continue...then substitute back in...OK?

3. ## Re: Algebraic Ratio

Ah yes that does make it simpler.

But I think where I'm having trouble is simplifying after performing certain steps

For example (working within the second term), (a/b - c/b) = [(ab - cb) / b^2] = [(a - c )/ b], correct?

Then multiplying this by b = [(ba - bc)/b]?

4. ## Re: Algebraic Ratio

Originally Posted by Albatrossie
Ah yes that does make it simpler.
But I think where I'm having trouble is simplifying after performing certain steps
For example (working within the second term), (a/b - c/b) = [(ab - cb) / b^2] = [(a - c )/ b], correct?
Then multiplying this by b = [(ba - bc)/b]?
Relax man!
b * [(a - c )/ b] = a - c ; over and out!

5. ## Re: Algebraic Ratio

So then, the second term end up = -c/2?

6. ## Re: Algebraic Ratio

No.
a - (a-c) / 2
= (2a - (a-c)) / 2
= (2a - a + c) / 2
= (a + c) / 2

And the 1st term: (a - c) / b

Since (a + c)(a - c) = a^2 - c^2, then ?????????????

7. ## Re: Algebraic Ratio

Where does the 2a come from??

8. ## Re: Algebraic Ratio

RULE: a + b/c = (ac + b) / c

9. ## Re: Algebraic Ratio

Thanks for the help! Took some time but got there in the end

10. ## Re: Algebraic Ratio

What are the steps involved in solving for b is this:

a + ab = 2b

11. ## Re: Algebraic Ratio

Originally Posted by Albatrossie
What are the steps involved in solving for b is this:
a + ab = 2b
Get the b terms together:
2b - ab = a
Factor:
b(2 - a) = a
Isolate b:
b = a / (2 - a)

Do some learning on your own:
Introduction to Algebra