# Tagged Questions

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

53 views

### Simplification of $\sum_{k=1}^n \frac{1}{4k^2-1}$

So I want to simplify this expression: $$\sum_{k=1}^n \frac{1}{4k^2-1}$$ and Wolfram Alpha tells me it can be simplified to two forms: $$\frac{n}{2n+1}$$ and $$\frac{1}{2}-\frac{1}{2(2n+1)}$$ The ...
50 views

### Factors that Impact a Weighted Average the Most

I am trying to determine how to calculate the factors that have the most significant impact on a weighted average. For example, let's say I am reviewing the number of patients that responded to a ...
101 views

### Why Does $f(x) = x\sqrt{x+3}$ Only Have One Critical Point?

I am trying to find the critical points of the function $f(x) = x\sqrt{x+3}$, then by using the First Derivative Test, determine which ones are a local maximum, local minimum, or neither. Using the ...
128 views

19 views

### Find a common denominator

I'm trying to integrate a function but first I need to find a common denominator for: $\frac{A}{x-8}\$ + $\frac{B}{x+1}\$ + $\frac{C}{x-1}\$
134 views

28 views

45 views

### Rules for solving inequalities with negative fractions

What are the algebraic rules for solving inequalities with negative signs and fractions like: $$\frac{1}{x}<-\frac{1}{5}$$
233 views

145 views

### Subtracting or Multiplying Fractions 3/4-1/2

This is the given scenario to help visualize the problem at hand. A bird feeder is filled with 3/4 of a full bag of seeds. The birds ate 1/2 of what was in the bird feeder. What fraction of a full ...
22 views

### Inequality relationship when additing a constant to the denominators

When $\frac{a}{b}>\frac{c}{d}$ where $a, b, c,$ and $d$ are positive real numbers, is $\frac{a}{b+1}>\frac{c}{d+1}$ true?
109 views

### Reasoning and Explanation for $2/3-1/2$

Denise says that $2/3-1/2 = 1/3$ and gives the reasoning indicated in Figure (below) to support her answer. Is Denise right? If not, what is wrong with her reasoning and how could you help her ...
So I have these fractions I need to merge together and shorten: $$\frac{1}{2a+8} + \frac{4}{a^2-16} + \frac{4}{a-4}$$ I understand that I need to make the denominators the same so that I can merge ...