Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [algebra-precalculus]

For questions about algebra and precalculus topics, which include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomial, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

This tag is for questions typically taught in precalculus, as well as elementary algebra.

These topics include linear, exponential, logarithmic, polynomial, rational, and trigonometric functions; conic sections, binomials, surds, graphs and transformations of graphs, solving equations and systems of equations; and other symbolic manipulation topics.

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Subtracting rational functions

I'm trying to find out how to solve this: $$\frac{x-2}{x^2+2x} - \frac{x+2}{x^2-2x} - \frac{4x}{x^2-4}$$ The answer is $\displaystyle \frac{-4}{x-2}$ What is this called? And is there any video of it on http://www.khanacademy.org ? Thanks!
Muazam
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Solving $a + \frac1a = 12$

I recently came across this problem in a textbook and I have no idea how to solve it : $$a + \frac1a = 12$$ Here is what I tried: $$\begin{align} a + \frac1a &= 12 \tag1\\[4pt] a^2 + 1 &= 12a \tag2 \\[4pt] a + 1 &= 3.4641a \tag3 \\[4pt] 1 &= 2.4641a…
Abhishek Singh
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How does this algebraically simplify to reach this result?

A problem I saw in my textbook uses the following logic to simplify an equation. $$\frac{m}{2}(m+1)+(m+1)\cdot\frac{2}{2}$$ $$=\frac{m+1}{2}(m+2)$$ $$=\frac{m+1}{2}[(m+1)+1]$$ The problem that I'm having is that I do not understand how the first…
October171
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Solving the equation $11x^2-6000x-27500 =0$, preferably without the quadratic formula

I obtained this form while solving an aptitude question. $$\frac{3000}{x-50} + \frac{3000}{x+50} = 11$$ I changed it into quadratic equation $$11x^2 -6000x - 27500 =0$$ but I don't know how to solve it. I can't find two factor for 303500 that sums…
Dineshkumar
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Do only many-one functions cross its horizontal asymptote?

Informal definitions: many-one, rational function and asymptote Many-one: For a function $f: A \to B$, If two o more elements of A, let's say, $a_{1}$ and $a_{2}$ have the same image in $B$, the function is referred to as a many-one function, also…
Nameless
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How to proceed solving $(7+4\sqrt3)^m+(7-4\sqrt3)^m=14$?

I have$$(7+4\sqrt3)^m+(7-4\sqrt3)^m=14$$ By noticing that $7+4\sqrt3=\frac1{7-4\sqrt3}$ one way to solve the equation is using substitution $(7+4\sqrt3)^m=t$ and solve for $t$ in $t+\frac1t=14$. But I'm trying to use a little different approach: We…
Amirali
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How to Factorise these expressions?

I'm dong some Factorisation revision and I'm a bit stuck. I've never done this before and I'm stuck a bit. First of all I know how to do small factorisations and I know you have to find the Highest Common Factor and that it's the opposite of…
user61406
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How to define the amount of additions. E.g. $1+2+3+4+5+6+7+8+9$

How to define the amount of additions. E.g. $1+2+3+4+5+6+7+8+9$ Are there $9$ additions, because of the nine numbers that are added together. Or can you also say that there are $8$ additions, because there are only $8$ '$+$' signs.
user8005
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Equation with high exponents

I would appreciate any help with this problem: $ x^8+2x^7+2x^6+5x^5+3x^4+5x^3+2x^2+2x^1+1x^0=0 $ I know that when $x$ isn't zero $x^0=1$ so the equation could be re-written as $ x^8+2x^7+2x^6+5x^5+3x^4+5x^3+2x^2+2x+1=0 $. I am not sure what to do…
suomynona
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Solve $(x+1)^{63}+(x+1)^{62}(x-1)+\cdots+(x-1)^{63}=0$

I want to find the solutions of $(x+1)^{63}+(x+1)^{62}(x-1)+\cdots+(x-1)^{63}=0$. It is not hard to see $x=0$ is a root of the equation. but I don't know how to solve this equation in general. I can see terms of the equation looks very similar to…
Etemon
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Calculate $x^3 + \frac{1}{x^3}$

Question $x^2 + \frac{1}{x^2}=34$ and $x$ is a natural number. Find the value of $x^3 + \frac{1}{x^3}$ and choose the correct answer from the following options: 198 216 200 186 What I have did yet I tried to find the value of $x + \frac{1}{x}$.…
Abhigyan Kumar
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mixture problem

From Stewart, Precalculus, $5$th ed, p.$71$, q.$55$ The radiator in a car is filled with a solution of $60\%$ antifreeze and $40\%$ water. The manufacturer of the antifreeze suggests that, for summer driving, optimal cooling of the engine is…
Ben
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Work-Time Problem

$10$ cats can eat $10$ mice in $20$ minutes. $2$ cats started eating $60$ mice in $3$ minutes, then another $6$ cats were added, how many more minutes will it take them to consume the remaining mice? I got the answer as $149.25$ minutes. But it…
Train Heartnet
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quadratic equation precalculus

from Stewart, Precalculus, 5th, p56, Q. 79 Find all real solutions of the equation $$\dfrac{x+5}{x-2}=\dfrac{5}{x+2}+\dfrac{28}{x^2-4}$$ my…
Ben
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what is the sum of this?$\frac12+ \frac13+\frac14+\frac15+\frac16 +\dots\frac{1}{2012}+\frac{1}{2013} $

What is the sum of $$\frac12+ \frac13+\frac14+\frac15+\frac16 +\dots\frac{1}{2012}+\frac{1}{2013} $$
Veritas
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