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.

47234 questions
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How do I define my function?

I have this function here. $$f(x)=\frac{\frac{x-14}{x-2}-1}{7+ \frac{4}{x-2} }$$ I can see that when $x=2$ and when $$x=\frac{10}{7}$$ it's undefined. But when I simplify this into this:$$ f(x)=\frac{-12}{7x-10}$$ $x=10/7$ is still not defined,…
Håkan Mjölk
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Applying binomial expansion and using algebra to find the value of $a+b$

Q) In the expansion of $f(x)=(1 + ax)^4 (1 + bx)^5$ where $a$ and $b$ are positive integers, the coefficient of $x^2$ is 66. Evaluate $a+b$. My working: After expanding the expression I simplified it and got $5b^2+10ab+3a^2=33$ After further…
Acid
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$x^{x\sqrt{x}} = (x\sqrt{x})^x$: How can I correctly explain the existence of the root $x=1$?

This is a fairly well-known equation: $x^{x\sqrt{x}} = (x\sqrt{x})^x$ $$x^{x\sqrt{x}} = (x\sqrt{x})^x \iff x^{x^{3/2}}=(x^{3/2})^x \iff x^{x^{3/2}}=(x^{3x/2})$$ Take logarithms on both sides: $$x^{3/2}\ln{x}=\frac{3x}{2}\ln{x}$$ From here it is…
QLimbo
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How to simplify $\frac{1-\frac{1-x}{1-2x}}{1-2\frac{1-x}{1-2x}}$?

$$\frac{1-\frac{1-x}{1-2x}}{1-2\frac{1-x}{1-2x}}$$ I have been staring at it for ages and know that it simplifies to $x$, but have been unable to make any significant progress. I have tried doing $(\frac{1-x}{1-2x})(\frac{1+2x}{1+2x})$ but that…
maxmitch
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Simplifying $\left({\sqrt{x} + \frac{1}{\sqrt{x}}}\right)^2 - \left({\sqrt{x} - \frac{1}{\sqrt{x}}}\right)^2 $

Hi can someone help me please simplify the following showing the working out step by step? $$ \left({\sqrt{x} + \frac{1}{\sqrt{x}}}\right)^2 - \left({\sqrt{x} - \frac{1}{\sqrt{x}}}\right)^2 $$ I can't get the answer matching the text book but I'd…
BIOS
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no. of solution of the equation $[x]^2+a[x]+b = 0$ is

If $a$ and $b$ are odd integer. Then the no. of solution of the equation $[x]^2+a[x]+b = 0$ is where $[x] = $ greatest Integer function My Try:: Let $[x] = y$. Then equation become $y^2+ay+b = 0$ Now If given equation has real Roots, Then…
juantheron
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How would I graph this?

How would I graph this: $t^2+3t=40$? I tried factoring $(t-5)(t+8)=0$ but I am not sure how to graph it because the function equals zero. I know how to do it if it is $y=t^2+3t-40$. I am probably overlooking the obvious, any help? Thanks
A A
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Am trying to fit a gas strut to some brackets. Think I have an equation to work it out, but not sure where to next.

I am trying to work out where to fit the pins on a gas strut for a 90 degree opening hinge. BTW - I am a farmer, not a maths person and this is my first post. Strut details: Open length is $325mm$. Closed length is $205mm$. Hinge goes from $0^\circ$…
user2991620
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Spivak Prologue, Chapter 2, problem 7: prove $\sum_{i=1}^n k^p$ can always be written as sum of powers of n

This is problem 7 of Spivak's Calculus, 4th Edition, Prologue Chapter 2: Show that $$\sum_{i=1}^n k^p$$ can always be written in the form $$\frac{n^{p+1}}{p+1} + An^{p} + Bn^{p-1} + Cn^{p-2} + ...$$ There is also a hint to use the method from…
xoux
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Where does the function $f(x) = \frac{2x}{x - 7}$ have an increasing slope?

Where does the function $f(x) = \frac{2x}{x - 7}$ have an increasing slope? $a. x \le 0, x > 7$ $b. x<7$ $c. x > 7$ $d. x \in \Bbb R, x \neq 7$ This question is from a test of mine in a pre-calculus course (so no calculus allowed in answering the…
Cisplatin
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Solve equation $\sqrt{s+13} - \sqrt{7-s} = 2$

Solve the equation $$\sqrt{s+13}-\sqrt{7-s} = 2$$ I moved the $-\sqrt{7-s}$ to the right side Thus, I had $$\sqrt{s+ 13} = 2 +\sqrt{7-s}$$ I then squared both sides $$\sqrt{s+ 13}^2 = \left(2 +\sqrt{7-s}\right)^2$$ Using the product formula $(x +…
Cetshwayo
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Finding all pairs $(m,n)$ of positive integers such that $m(n + 1) + n(m − 1) = 2013$

Find all pairs $(m, n)$ of positive integers such that $$m(n + 1) + n(m − 1) = 2013$$ What I've done: I tried to make the problem simpler by $2mn+m-n$ and factoring it equals $(2m-1)(2n+1)$ Where do I go now?
QuantumPi
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A problem of "guessing number"

The problem statement: I have two people A and B, and think of a natural number n. Then I give the number n to A and the number n + 1 to B. I tell them that they have both been given natural numbers, and further that they are consecutive natural…
ChuNan
  • 303
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Find $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ if $a+b+c=0$

I'm stuck at this algebra problem, it seems to me that's what's provided doesn't even at all. Provided: $$a+b+c=0$$ Find the value of: $$\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$$ Like I'm not sure where to start, and the…
Spacy
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Solve $\sqrt{2x-5} - \sqrt{x-1} = 1$

Although this is a simple question I for the life of me can not figure out why one would get a 2 in front of the second square root when expanding. Can someone please explain that to me? Example: solve $\sqrt{(2x-5)} - \sqrt{(x-1)} = 1$ Isolate one…
Kalina Kama
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