query: Find all positive integral soludions of $\frac{a}{b+c} + \frac{b}{a+c} + \frac{c}{a+b} = 4$
positive_passages.docid: 50283
positive_passages.text: Find answer of $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=4$
negative_passages.docid: 18119
negative_passages.text: Show that if a,b,c,d are positive then $\frac{ab}{a+b}+\frac{cd}{c+d}\le \frac{(a+c)(b+d)}{a+b+c+d}$
negative_passages.docid: 52744
negative_passages.text: The value of a, b and c for this integral
negative_passages.docid: 31257
negative_passages.text: Let $a,b,c>0$ such that $a+b+c=3$, find max/min of $\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$
negative_passages.docid: 147648
negative_passages.text: Proving $\frac{a}{a^2-a+1}+\frac{b}{b^2-b+1}+\frac{c}{c^2-c+1}+\frac{d}{d^2-d+1}\le \frac{8}{3}$ given $a+b+c+d=2$
negative_passages.docid: 6830
negative_passages.text: Find $\int\frac1x\sqrt\frac{1-x}{1+x}\ dx$
negative_passages.docid: 118507
negative_passages.text: Prove $\frac{ab}{1+c^2}+\frac{bc}{1+a^2}+\frac{ca}{1+b^2}\le\frac{3}{4}$ if $a^2+b^2+c^2=1$
negative_passages.docid: 30307
negative_passages.text: Find the value of $k$ in $\frac{b+c}{\sqrt{a}}+\frac{c+a}{\sqrt{b}}+\frac{a+b}{\sqrt{c}} \ge \sqrt{a}+\sqrt{b}+\sqrt{c}+k$
negative_passages.docid: 112565
negative_passages.text: Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{9}{a+b+c} : (a, b, c) > 0$
negative_passages.docid: 26287
negative_passages.text: Find $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ if $a+b+c=0$
negative_passages.docid: 52672
negative_passages.text: Solution of $\frac{a}{b}=\frac{a'}{b'}$ if $a,b,a',b' \in \mathbb{N}$
negative_passages.docid: 153241
negative_passages.text: Four different positive integers a, b, c, and d are such that $a^2 + b^2 = c^2 + d^2$
negative_passages.docid: 140290
negative_passages.text: Solving $AB - BA = C$
negative_passages.docid: 52204
negative_passages.text: Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
negative_passages.docid: 57686
negative_passages.text: Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
negative_passages.docid: 79
negative_passages.text: Find $a$, $b$ and $c$ that satisfy the following equations
negative_passages.docid: 15116
negative_passages.text: Proof of the inequality $\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b} \geq \frac{3}{2}$