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Ok So I am about to take the accuplacer college level math for a college but I do not understand this problem on the practice packet. Honestly I am blank on this problem and need help step by step on how to solve it.Please help me understand it. Thanks in advance

If a ≠ b and 1/x + 1/a= 1/b , then x =

A. 1/b – 1/a

B. b – a

C. 1/ab

D. a – b/ab

E. ab/a – b

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up vote 5 down vote accepted

It is asking you to solve for $x$, given that $$\frac{1}{x} +\frac{1}{a}=\frac{1}{b}.$$

To solve for $x$, first isolate $x$ by itself on one side; for example, move that $\frac{1}{a}$ to the right. That will give you an equation of the form $$\frac{1}{x} = \text{stuff}.$$

Do the operation on the right, and then take reciprocals (or cross-multiply) to get an expression for $x$ in terms of $a$ and $b$. Then figure out which of the five options given is that expression for $x$.

You can the work as an edit to your question and we can tell you if you are doing it right or not; that will help you learn better than me doing it for you.

(For extra points, figure out exactly on which step you need to assume $a\neq b$...)

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Clearly explained and brief still! +1. – Joe May 3 '12 at 3:52
So the equal sign (=) with a slash (/) means if a and b are "not equal" – Backtrack May 3 '12 at 4:02
@Backtrack... Ehr... yes. If you were unsure about the symbols, you should have mentioned that explicitly. – Arturo Magidin May 3 '12 at 4:04
Yes I will try this tomorrow morning and you guys can check my work. But anyway yes, the fractions are throwing me off. To isolate x should I divide 1/a by itself and also by 1/b? And then after that what? And also should I leave the letters how they are? – Backtrack May 3 '12 at 4:25
@Backtrack: To isolate $x$, you first move the $\frac{1}{a}$ to the right; This does not involve divisions of any kind, just additions/subtractions. Then you will have an expression on the right that has no $x$'s in it: just $1$s, $a$s, and $b$s. Do the operation, which will be a sum/subtraction of fraction, and write the answer as a single fraction. You should get something along the lines of $$\frac{1}{x} = \frac{\text{expression1 involving }a\text{ and }b}{\text{expression2 involving }a\text{ and }b}.$$ Then you can cross multiply to get $x$ equal to something. – Arturo Magidin May 3 '12 at 4:28

You need to solve the equation for $x$, but I imagine the fractions are throwing you off. You can get rid of the fractions by multiplying both sides by $abx$ (why? because this is the least common multiple of $a,b$, and $x$), then it's simple algebra to rearrange and solve for $x$. Do you see why it's necessary for $a\neq b$?

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