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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

2 Answers 2

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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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    @Backtrack: You use *algebra*. $\frac{a}{b}+\frac{c}{d} = \frac{ad}{bd} + \frac{cb}{db} = \frac{ad+bc}{bd}.$ Doesn't matter if the numerators are "numbers" or "letters", it's algebra all the way down.2012-05-03
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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 $a\neq b$?