Question

The value of x that satisfies the equation $\frac{4}{x-3}+\frac{5}{x-5}=\frac{9}{x-13}$ is

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is A $4$

Solve for x:

$\frac{4}{x-3}+\frac{5}{x-5}=\frac{9}{x-13}$

$⟹\frac{4x-20+5x-15}{(x-3)(x-5)}=\frac{9}{x-13}$

$⟹\frac{9x-35}{(x^2-8x+15)}=\frac{9}{x-13}$

$⟹(9x-35)(x-13)=9(x^2-8x+15)$

$⟹9x^2-117x-35x+455=9x^2-72x+135$

$⟹-152x+455=-72x+135$

$⟹320=80x$

$⟹x=4$