# Tagged Questions

Questions on fractions, which are expressions (not values) of the form $\frac pq$.

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### Partial Fractions Question: $\frac1{s(n-s)}$

How do you decompose the fraction $$\frac1{s(n-s)}$$ to two fractions? ($s$ and $n$ are variables).
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### Laplace Transform for Solving Differential Equation

I solved the following task, but since I am new in this field I need to check if it is correct or if there is anything I am missing or doing wrong. Task : Solve differential equation using Laplace ...
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### Quotient field of gaussian integers

Let $D$ be the set of all gaussian integers of the form $m+ni$ where $m,n \in Z$. Carry out the construction of the quotient field $Q$ for this integral domain. Show that this quotient field is ...
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### Adding fractions of Groups of People

I understand the rules of adding fractions perfectly well. I know how to find common denominators, and understand why adding fractions without common denominators doesn't make sense. But, today ...
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### If you take the reciprocal in an inequality, would it change the $>/<$ signs?

Example:$$-16<\frac{1}{x}-\frac{1}{4}<16$$ In the example above, if you take the reciprocal of $$\frac{1}{x}-\frac{1}{4} = \frac{x}{1}-\frac{4}{1}$$ would that flip the $<$ to $>$ or ...
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### Simplify the following expression

$$\left(\frac{4}{27}\right)^{3/2}$$ I am trying to figure out how to solve this problem and my teacher was not explaining it well enough for me to grasp it. Can anybody maybe help me with step-by-...
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### Finding LCM of an expression

Image link I am currently trying to figure out how to solve this problem. I know how they got the denominator but am unsure how they got 6x in the numerator? Can somebody explain this to me?
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### What happens when you add $x$ to $\frac{1}{3}x$?

I am dealing with an equation that requires me to add $x$ to $\frac{1}{3}x$: $x + \frac{1}{3}x$ = ?? I know this might be simple to any of you on this site, because you are all asking questions with ...
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### Bob and Jim's Coins [closed]

Bob had 52 more coins that Jim after Jim gave 1/5 of his coins to him. If they had 260 coins total, how many coins did Bob have at first?
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### When is $\sqrt{x/y^2}$ equal to $\sqrt{x}/y$?

The solution to the quadratics is given by $r = -\dfrac{b}{2a}\pm\sqrt{\dfrac{b^2-4ac}{4a^2}}$, which is shortened to $r = -\dfrac{b}{2a}\pm\dfrac{\sqrt{b^2-4ac}}{2a}$, but I'm wondering how if this ...
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### Detecting that a fraction is a repeating decimal

Given any fraction where both the numerator (N) and denominator (D) are both positive and are both whole numbers. Without manually dividing N by D, is it possible to pre-determine if the resulting ...
$$a = x + \frac1x \\b =y + \frac1y \\ c = xy +\frac1{xy}$$ Express $c$ in terms of $a$ and $b$