# Thread: [SOLVED] Basic help with transposing in linear equation!

1. ## [SOLVED] Basic help with transposing in linear equation!

b needs to be transposed in the following:

a = sqrt(b / b+c)

It will become:

a^2 = b / b+c

Then I can cancel out b+c by multiplying it on both sides:

a^2 (b+c) = b / b+c x b+c
b = a^2b + a^2c

^ that's what I get, but it isn't the answer .. Help please

2. Originally Posted by struck
b needs to be transposed in the following:

a = sqrt(b / b+c)

It will become:

a^2 = b / b+c

Then I can cancel out b+c by multiplying it on both sides:

a^2 (b+c) = b / b+c x b+c
b = a^2bc

^ that's what I get, but it isn't the answer .. Help please
$\displaystyle a=\sqrt\frac{b}{b+c}$
$\displaystyle \therefore a^2 = \frac {b}{b+c}$
$\displaystyle \therefore (a^2)(b+c)=b$
$\displaystyle \therefore a^2b+a^2c = b$
$\displaystyle \therefore a^2c = b - a^2b$
$\displaystyle \therefore a^2c = b(1-a^2)$
$\displaystyle \therefore b= \frac{a^2c}{1-a^2}$

3. Thanks, that helps. Actually I reached till the 4th step. Wrote it wrong in the post. In the second step, shouldn't it be this or am I not understanding it *confused* :
$\displaystyle \therefore a^2 = \frac {b}{b+c}$

So that means factorization is compulsory in this case? Is there any rule to when factorization is almost always necessary?

Ohh and does it means the answer is wrong if the answer contains the subject TO BE transposed, for example, b in this case.

4. Originally Posted by struck
Thanks, that helps. Actually I reached till the 4th step. Wrote it wrong in the post. In the second step, shouldn't it be this or am I not understanding it *confused* :
$\displaystyle \therefore a^2 = \frac {b}{b+c}$

So that means factorization is compulsory in this case? Is there any rule to when factorization is almost always necessary?

Ohh and does it means the answer is wrong if the answer contains the subject TO BE transposed, for example, b in this case.
Yes, it was meant to be that, typo error, i've corrected it now.

Factorization is compulsory when you have 2 or more of the same variable (letter) so that it can be made on it's own.

No, the answer is not wrong. Some question may ask for the answer of b, in which case arranging has to be done, then the calculation.