Category: Algebra

Question Number 218003 by hardmath last updated on 25/Mar/25 $$1.\int \frac{\mathrm{x}\mathrm{dx}}{(\mathrm{x}+2)\cdot (\mathrm{x}+4)}$$$$2.\int \frac{\mathrm{x}+2}{{\mathrm{x}}^3-{2\mathrm{x}}^2}\mathrm{dx}$$$$3.\int \frac{2\mathrm{x}+7}{{\mathrm{x}}^2-4\mathrm{x}+3}\mathrm{dx}$$ Commented by Ghisom last updated on…

Question Number 217911 by Rasheed.Sindhi last updated on 23/Mar/25 $$Solve$$$${\left(\frac{x}{x-1}\right)}^2+{\left(\frac{x}{x+1}\right)}^2=6$$ Answered by Rasheed.Sindhi last updated on 23/Mar/25 $$\left(\frac{{x}}{{x}−\mathrm{1}}\right)^{\mathrm{2}} +\left(\frac{{x}}{{x}+\mathrm{1}}\right)^{\mathrm{2}}…

Question Number 217895 by hardmath last updated on 23/Mar/25 Commented by mr W last updated on 23/Mar/25 $$questioniswrong.C_n^{r}isonlydefined$$$$for0⩽r⩽n.$$ Commented…

Question Number 217887 by ArshadS last updated on 23/Mar/25 $$Solve:$$$$\frac{x+1}{x-2}+\frac{x-1}{x+2}=\frac{2x+1}{x-1}+\frac{2x-1}{x+1}$$ Answered by Rasheed.Sindhi last updated on 23/Mar/25 $$\frac{x+1}{x-2}-1+\frac{x-1}{x+2}-1+2=\frac{2x+1}{x-1}-2+\frac{2x-1}{x+1}-2+4$$$$\frac{\mathrm{3}}{{x}−\mathrm{2}}+\frac{−\mathrm{3}}{{x}+\mathrm{2}}=\frac{\mathrm{3}}{{x}−\mathrm{1}}+\frac{−\mathrm{3}}{{x}+\mathrm{1}}+\mathrm{2} \…

Question Number 217940 by ArshadS last updated on 23/Mar/25 $$Solve$$$$\sqrt{2x+7}-\sqrt{x-1}=2$$ Answered by Frix last updated on 23/Mar/25 $$\mathrm{No}\mathrm{real}\mathrm{solution}\mathrm{because}\min \left(\mathrm{lhs}\right)>2$$$${a},\:{b}\:\in\mathbb{R}\wedge{b}\neq\mathrm{0} \…