$7r^{2}+41r+30$

$\lim_{x\to\infty}\ln\left(5x^2-3x\right)-\ln\left(x^2+1\right)$

$\frac{12}{x-5}=\frac{3}{x-5}-3$

$\lim_{x\to\frac{\pi}{4}}\left(\frac{cos\left(2x\right)}{\cos\left(x\right)-\sin\left(x\right)}\right)$

$\frac{12}{17}x\left(-\:\frac{12}{25}\right)x\:\frac{1}{6}$

$g\left(x\right)=-x^3+1$

$\frac{x^{2}+3x+5}{x+1}$