Question

Solve for $x:\frac{x^2-36}{x^2-64}=\frac{100}{49}$

Answer 1

$\frac{x^2-36}{x^2-64}=\frac{100}{49}$

$\Rightarrow 49(x^2-64)=100(x^2-36)$

$\Rightarrow 49x^2-3136‬=100x^2-3600$

$\Rightarrow 100x^2-49x^2=3600-3136$

$\Rightarrow 51x^2=564$

$\Rightarrow x^2=\frac{564}{51}$

$\therefore x=\pm \sqrt{\frac{188}{17}}$