Maths Question

[quizzkid]

Hi I need help with this maths question please. I never was good at algebra.
A= 3b+2 over b+1 give formula for b Help!!

[Fibonacci]

A = 3b + 2/ b+1
multiply both sides by b+1
gives Ab + A = 3b +2
rearranging
gives Ab - 3b = 2 - A
factorise RHS b(A-3) = 2 - A
now divide both sides by A-3
gives b = (2-A) over (A-3)

[jim360]

First thing to do whenever you are presented with a fraction is to get rid of the fraction. Here the way to do that is multiply both sides by (b+1), giving:

A*(b+1) = [(3b+2)/(b+1)]*(b+1)

On the right-hand side the b+1 on the top and bottom of the fraction cancel, leaving just 3b+2. So:

A*(b+1) = (3b+2)

Now expand the brackets on the left, as A*(b+1) = A*b + A*1 = A*b + A, leaving:

A*b + A = 3b+2

Next, we want to rearrange for b, so move everything that has a b in it to one side, and anything that doesn't have a b in it to the other. Here we should subtract A from both sides, and also subtract 3b from both sides, cancelling the A on the left and the 3b on the right:

A*b + A - A - 3b = 3b - 3b + 2 - A

or A*b - 3b = 2-A

Now just as A(b+1) = A*b + A, we can replace A*b - 3b by b*(A-3) (you can see this be expanding the brackets again). Hence the equation becomes

b*(A-3) = 2-A

Finally, we must divide both sides by A-3, removing it from the left-hand side, and leaving:

b*(A-3)/(A-3) = (2-A)/(A-3)

or just

b = (2-A)/(A-3)

Guiding principle: do whatever you want to both sides of the equation, but make sure you do exactly the same thing on both sides. Hence add A to both, or subtract A from both, or divide both sides by b or multiply both sides by 2, but always do the same thing on both sides.

[factor-fiction]

(b+1)A=3b+2
bA +A= 3b+2
bA-3b= 2-A
b(A-3)= 2-A

b= (2-A)/(a-3)

Same as Fibaonacci

[factor-fiction]

Sorry jim, I hadn't seen yours

[quizzkid]

Thank you all so much for your help. Hopefully I will be able to sort out the rest of them from your explanations.

[jim360]

You're welcome and do feel free to ask any other questions you might have. Hope the explanations are useful, though.