Answer
$$\lim_{x\to-5^-}\frac{3x}{2x+10}=\infty$$
Work Step by Step
$$A=\lim_{x\to-5^-}\frac{3x}{2x+10}=\lim_{x\to-5^-}\frac{(3x+15)-15}{2x+10}=\lim_{x\to-5^-}\frac{3(x+5)-15}{2(x+5)}$$
$$A=\lim_{x\to-5^-}\Big(\frac{3}{2}-\frac{15}{2(x+5)}\Big)=\frac{3}{2}-\lim_{x\to-5^-}\frac{15}{2x+10}$$
As $x\to-5^-$, $2x+10$ approaches $0$ from the left, where $(2x+10)\lt 0$, so $15/(2x+10)$ will approach $-\infty$. Therefore,
$$A=\frac{3}{2}-(-\infty)=\infty$$
