query: Understanding the simplification $\frac{x(x-1)}{x-1} = x$
positive_passages.docid: 29263
positive_passages.text: Can not understand simplification of equation
negative_passages.docid: 80004
negative_passages.text: Why is $1/i$ equal to $-i$?
negative_passages.docid: 93813
negative_passages.text: How to show that $\sum\limits_{k=0}^n (-1)^k\tfrac{{ {n}\choose{k}}}{{ {x+k}\choose{k}}} = \frac{x}{x+n}$
negative_passages.docid: 104583
negative_passages.text: Simplify $\int \frac{1}{\sqrt{2-x^2}}\, dx$
negative_passages.docid: 53519
negative_passages.text: Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
negative_passages.docid: 89056
negative_passages.text: Intuitive understanding of ideal $I = (x+1,x^2+1)$ and the quotient $\Bbb Z[x]/I$
negative_passages.docid: 41779
negative_passages.text: Is $x/x$ equal to $1$
negative_passages.docid: 78471
negative_passages.text: Closure of $\{\frac{1}{n}\}:=M$
negative_passages.docid: 72906
negative_passages.text: Is $\frac{\partial}{\partial x_1}=\frac{\partial}{\partial y_1}$ if $x_1=y_1$?
negative_passages.docid: 3356
negative_passages.text: Why $\sum_{k=0}^m x^k $ is equal to $\dfrac{x^{m+1}-1}{x-1} $?
negative_passages.docid: 36083
negative_passages.text: If $k > 1$, then $\frac1{(k - 1)^2}-\frac1{(k + 1)^2}=\frac{4k}{(k^2 - 1)^2}$, hence simplify $\sum\limits_{k = 2}^n\frac k{(k^2 - 1)^2}$
negative_passages.docid: 104646
negative_passages.text: Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
negative_passages.docid: 84597
negative_passages.text: Derivative of $(1-x)^{-2}$
negative_passages.docid: 15164
negative_passages.text: Proof of $\sum^{2N}_{n=1} \frac{(-1)^{n-1}}{n} = \sum^{N}_{n=1} \frac{1}{N+n}$
negative_passages.docid: 77076
negative_passages.text: Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
negative_passages.docid: 46310
negative_passages.text: Showing that $ \int_{0}^{1} \frac{x-1}{\ln(x)} \mathrm dx=\ln2 $
negative_passages.docid: 56032
negative_passages.text: How come $\frac{1}{1-x}$ and $\frac{x}{1-x}$ have the same derivative?