query: Can someone help me with this algebraic inequality?
positive_passages.docid: 124868
positive_passages.text: Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
negative_passages.docid: 143968
negative_passages.text: Proving this inequality by mathematical induction
negative_passages.docid: 53123
negative_passages.text: Trying to derive a contradiction with this simple inequality,
negative_passages.docid: 136290
negative_passages.text: a mathematical problem on inequalities
negative_passages.docid: 66261
negative_passages.text: Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$
negative_passages.docid: 90343
negative_passages.text: Proving the inequality $|e^z-1|\leq e^{|z|}-1$
negative_passages.docid: 20863
negative_passages.text: how do I prove this inequallity?
negative_passages.docid: 156513
negative_passages.text: Prove that inequality $\sum _{cyc}\frac{a^2+b^2}{a+b}\le \frac{3\left(a^2+b^2+c^2\right)}{a+b+c}$
negative_passages.docid: 156669
negative_passages.text: Trying to prove a simple (?) inequality
negative_passages.docid: 115335
negative_passages.text: How can we prove this integral inequality?
negative_passages.docid: 135550
negative_passages.text: Inequality question­
negative_passages.docid: 73987
negative_passages.text: Prove the inequality $({1+\frac{a}b})^n$ + $(1+\frac{b}a)^n$ $\geq$ $2^{n+1}$
negative_passages.docid: 5465
negative_passages.text: This inequality $a+b^2+c^3+d^4\ge \frac{1}{a}+\frac{1}{b^2}+\frac{1}{c^3}+\frac{1}{d^4}$
negative_passages.docid: 156555
negative_passages.text: Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
negative_passages.docid: 140299
negative_passages.text: Inequality based on triangle: $\frac{3}{2}\le\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$
negative_passages.docid: 30044
negative_passages.text: Inequality with triangle sides
negative_passages.docid: 83386
negative_passages.text: Inequality with exponents $x^x+y^y \ge x^y +y^x$