Question

If $\frac{4}{x+1}+\frac{5}{x+3}=\frac{9}{x+2}$ then the value of $x$ is :

Answer 1

$\frac{4}{x+1}+\frac{5}{x+3}=\frac{9}{x+2}\Rightarrow \frac{4(x+3)+5(x+1)}{(x+1)(x+3)}=\frac{9}{(x+2)}(9x+17)(x+2)=9(x+1)(x+3)\Rightarrow 9x^{2}17x+18x+34=9(x^2+4x+3)9x^2+35x+34=9x^2+36x+27\Rightarrow 34-27=36x-35x\Rightarrow x=7$