query: A solution to the equation $\frac{1}{x}=0$
positive_passages.docid: 22310
positive_passages.text: Why not to extend the set of natural numbers to make it closed under division by zero?
negative_passages.docid: 19561
negative_passages.text: Why is $\frac{1}{\frac{1}{X}}=X$?
negative_passages.docid: 146594
negative_passages.text: Prove that $\frac{d}{dx}(\tan^{-1}(x))=\frac{1}{1+x^2}dx$
negative_passages.docid: 82286
negative_passages.text: Derivation of asymptotic solution of $\tan(x) = x$.
negative_passages.docid: 27969
negative_passages.text: Why does $\frac{1}{x} < 4$ have two answers?
negative_passages.docid: 42713
negative_passages.text: Solutions to the equation $ze^{a-z}=1$
negative_passages.docid: 10753
negative_passages.text: Natural number solutions to $\frac{xy}{x+y}=n$ (equivalent to $\frac 1x+\frac 1y=\frac 1n$)
negative_passages.docid: 145504
negative_passages.text: Help solving variable separable ODE: $y' = \frac{1}{2} a y^2 + b y - 1$ with $y(0)=0$
negative_passages.docid: 9143
negative_passages.text: Solve $u_{xx}-3u_{xt}-4u_{tt}=0$ where $u(x,0)=x^2$ and $u_t(x,0)=e^x$
negative_passages.docid: 76175
negative_passages.text: Does the equation have a real solution...please help!
negative_passages.docid: 87055
negative_passages.text: How to prove $\frac{x}{1+x^2}0$?
negative_passages.docid: 61782
negative_passages.text: How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
negative_passages.docid: 21846
negative_passages.text: Let p be a prime. Consider the equation $\frac1x+\frac1y=\frac1p$. What are the solutions?
negative_passages.docid: 129454
negative_passages.text: Solution to a quadratic form
negative_passages.docid: 13533
negative_passages.text: Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
negative_passages.docid: 30697
negative_passages.text: Solution of a Riccati ODE
negative_passages.docid: 38894
negative_passages.text: Solve $x=y\frac{dy}{dx}-\left(\frac{dy}{dx}\right)^{2}$