Solve for a- given an equation involving a

The equation reads
----A·B
r=-------, solve for a
----A+B

Okay, so as I'm sure you've noticed, the forum does not preserve whatever formatting it is you tried to use. However, I'm assuming that you meant to type the expression \(\displaystyle r=\dfrac{A-B}{A+B}\). In the future that can be typeset either as r = (A - B)/(A + B) or by typing the following:

Code:
[tex]r=\dfrac{A-B}{A+B}[/tex]

Further, I'm assuming, pursuant to what Subhotosh Khan said that you made the common mistake of mixing up the variables a and A. In the world of math, capitals letters definitely matter, and a and A are regarded as completely different variables from one another. It is perfectly possible to encounter a problem which uses both these variables, and mixing them up would be disastrous.

With these assumptions out of the way, I'd begin by multiplying both sides by (A + B) to "clear" the fraction, leaving \(\displaystyle r(A + B)=A - B\). Now, what do you think would be a good next step to take? Please share with us any and all work you've done on this problem, even the parts you know for sure are wrong. Thank you.
 
The equation reads
----A·B
r=-------, solve for a
----A+B
Assuing that you're actually supposed to solve for A, and that the equation is meant to be as follows:

. . . . .\(\displaystyle r\, =\, \dfrac{A\, \cdot\, B}{A\, +\, B}\)

...the customary first step would be to multiply through, to clear the denominator. This will leave you with:

. . . . .\(\displaystyle r\, (A\, +\, B)\, =\, A\, \cdot\, B\)

Then multiply out the left-hand side, and then gather the terms containing the target variable on one side of the equation. (I'd gather then on the right-hand side.) Then factor out the target variable, and divide off whatever is left. Your answer should be in the form of a fraction.

If you get stuck, please reply with a clear listing of your thoughts and efforts so far. Thank you! ;)
 
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