Answer
$$\lim_{x\to\infty}\frac{2x+3}{5x+7}=\frac{2}{5}$$
Work Step by Step
*Remember that $\lim_{x\to\pm\infty}\frac{a}{x^n}=0$
$$A=\lim_{x\to\infty}\frac{2x+3}{5x+7}$$
Divide both numerator and denominator by the highest degree of $x$ in the denominator, which is $x$ in this case:
$$A=\lim_{x\to\infty}\frac{2+\frac{3}{x}}{5+\frac{7}{x}}$$
$$A=\frac{2+0}{5+0}=\frac{2}{5}$$
