 When the places holds a speech, teaching pronunciation : a course book and reference guide ebook celce murcia is additionally useful. You have remained in. Your browser does not support inline frames or is currently configured not to display inline frames. To view this page ensure that Adobe Flash Player version 10.0.0 or greater is installed.Q: Proving T is a linear function Define $T\colon \mathbb{R}\to \mathbb{R}$ $T(x)=\frac{2x^2+3x+2}{2x+3}$ Now I want to prove that $T$ is linear. Suppose $T(cx+y)=cT(x)+T(y)$ for all $x,y\in \mathbb{R}$. Using the above definition of $T$ we can say this is equivalent to $\frac{c(2x^2+3x+2)+(2x+3)(y^2+3y+2)}{c(2x+3)+2}=c\frac{2x^2+3x+2}{2x+3}+\frac{2x^2+3x+2}{2x+3}$. Now I want to show that this is equivalent to $\frac{c(2x^2+3x+2)+(2x+3)(y^2+3y+2)}{c(2x+3)+2}=c\frac{2x^2+3x+2}{2x+3}+\frac{2x^2+3x+2}{2x+3}$. What I have done, I am over thinking it: $\frac{c(2x^2+3x+2)+(2x+3)(y^2+3y+2)}{c(2x+3)+2}=c\frac{2x^2+3x+2}{2x+3}+\frac{2x^2+3x+2}{2x+3}$ \$c\frac{2x^2+3x+2}{2x+3}+\frac{2x^2+3x+2}{2x+3}=c\frac{c( 3e33713323