Simplify if a/b = 4/5 and b/c = 1516, then c^2 - a^2c^2 + a^2 is = ?

Answer: Option B

$$\begin{array}{rl}& \frac{a}{b}=\frac{4}{5}\text{ and }\frac{b}{c}=\frac{15}{16}\\ & \Rightarrow \left(\frac{a}{b}\times \frac{b}{c}\right)=\left(\frac{4}{5}\times \frac{15}{16}\right)\\ & \Rightarrow \frac{a}{c}=\frac{3}{4}\\ & \therefore \frac{c^2-a^2}{c^2+a^2}\\ & =\frac{1-\left(\frac{a^2}{c^2}\right)}{1+\left(\frac{a^2}{c^2}\right)}\\ & =\frac{1-{\left(\frac{a}{c}\right)}^2}{1+{\left(\frac{a}{c}\right)}^2}\\ & =\frac{1-\frac{9}{16}}{1+\frac{9}{16}}\\ & =\frac{\left(\frac{7}{16}\right)}{\left(\frac{25}{16}\right)}\\ & =\frac{7}{25}\end{array}$$