Discussion Forum

If $\frac{a}{b}=\frac{4}{5}$ and $\frac{b}{c}=\frac{15}{6}$, then $\frac{c^{2}-a^{2}}{c^{2}+a^{2}}$ is

Answer:

Explanation:

$\frac{a}{b}=\frac{4}{5}$ and $\frac{b}{c}=\frac{15}{6}$
$\Rightarrow\left(\frac{a}{b} \times \frac{b}{c}\right)-\left(\frac{4}{5} \times \frac{15}{6}\right)$
$\Rightarrow\frac{a}{c}=\frac{3}{4}$
$\therefore \frac{c^{2}-a^{2}}{c^{2}+a^{2}}=\frac{1-\left(\frac{a^2}{c^2}\right)}{1+\left(\frac{a^2}{c^2}\right)}$
$=\frac{1-\left(\frac{a}{c}\right)^2}{1+\left(\frac{a}{c}\right)^2}$
$=\frac{1-\frac{9}{16}}{1+\frac{9}{16}}$
$=\frac{7/16}{25/16}=\frac{7}{25}$