query: How is $\frac {x^2 + x - 6}{x - 2}$ different from $(x+3)$?
positive_passages.docid: 49368
positive_passages.text: Why does factoring eliminate a hole in the limit?
negative_passages.docid: 152895
negative_passages.text: What is wrong with this derivation of $\frac{d}{dx}x^2$?
negative_passages.docid: 14968
negative_passages.text: How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$
negative_passages.docid: 111705
negative_passages.text: Why does $\frac{1+t}{(1-t)^3}=\sum_{n=0}^{\infty}(1+n)^2t^n$
negative_passages.docid: 99502
negative_passages.text: Question on the coefficients of $(1+x+x^2+x^3+x^4)^{496}$
negative_passages.docid: 128749
negative_passages.text: Taylor's Remainder $x-\frac{x^2}{2}+\frac{x^3}{3(1+x)}<\log(1+x) <x-\frac{x^2}{2}+\frac{x^3}{3}$
negative_passages.docid: 120085
negative_passages.text: Compute $\int \frac{-3}{2x^2-x-1} dx$
negative_passages.docid: 33184
negative_passages.text: Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
negative_passages.docid: 24108
negative_passages.text: Proof of the equality $\sum\limits_{k=1}^{\infty} \frac{k^2}{2^k} = 6$
negative_passages.docid: 44630
negative_passages.text: Is $\frac{1}{\sqrt{2}}$ a fraction or not?
negative_passages.docid: 63191
negative_passages.text: What is the $k-$th derivative of $ \frac{1}{1-x^2}$?
negative_passages.docid: 146358
negative_passages.text: Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$?
negative_passages.docid: 117999
negative_passages.text: Prove by contradiction (not using a calculator) that $\sqrt6 + \sqrt2 < \sqrt{15}$?
negative_passages.docid: 56032
negative_passages.text: How come $\frac{1}{1-x}$ and $\frac{x}{1-x}$ have the same derivative?
negative_passages.docid: 114861
negative_passages.text: equation $\frac{\frac{1}{x^2}-\frac{1}{y^2}}{\frac{1}{x^2}+\frac{1}{y^2}}$
negative_passages.docid: 150417
negative_passages.text: Two apparently different antiderivatives of $\frac{1}{2 x}$
negative_passages.docid: 47325
negative_passages.text: Limit of quotients with square roots: $\lim_{x\to2} \frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}$