Question

Answer 1

\(a,C=\left[\dfrac{\left(x+1\right)\left(x+2\right)}{\left(x+2\right)\left(x-1\right)}-\dfrac{x^2+x}{x-1}\right]\cdot\dfrac{x-1+x+1}{\left(x-1\right)\left(x+1\right)}\left(x\ne\pm1;x\ne-2\right)\\ C=\dfrac{x+1-x^2-x}{x-1}\cdot\dfrac{2x}{x^2-1}\\ C=\dfrac{x^2-1}{1-x}\cdot\dfrac{2x}{x^2-1}=\dfrac{2x}{1-x}\\ b,C=\dfrac{2}{3}\Leftrightarrow\dfrac{2x}{1-x}=\dfrac{2}{3}\Leftrightarrow3x=1-x\\ \Leftrightarrow x=\dfrac{1}{4}\left(tm\right)\)