Question

Solve: $\frac{5}{x-5}+\frac{2}{x-2}=\frac{3}{x-3}+\frac{4}{x-4}$

• A. $0,\frac{5}{2}$
• B. $1,\frac{9}{2}$
• C. $2,\frac{11}{2}$
• D. None of these
  

Answer 1

Answer: (D)

None of these

The value of $\frac{5}{x-5}+\frac{2}{x-2}=\frac{3}{x-3}+\frac{4}{x-4}$ is

$\Rightarrow \frac{5(x-2)+2(x-5)}{(x-5)(x-2)}=\frac{3(x-4)+4(x-3)}{(x-3)(x-4)}$

$\Rightarrow \frac{5x-10+2x-10}{(x-5)(x-2)}=\frac{3x-12+4x-12}{(x-3)(x-4)}$

$\Rightarrow \frac{7x-20}{(x-5)(x-2)}=\frac{7x-24}{(x-3)(x-4)}$

$\Rightarrow (7x-20)(x-3)(x-4)=(7x-24)(x-5)(x-2)$

$\Rightarrow (7x^2-20x-21x+60)(x-4)=(7x^2-24x-35x+120)(x-2)$

$\Rightarrow 7x^3-41x^2+60x-28x^2+164x-240=7x^3-59x^2+120x-14x^2+118x-240$

$\Rightarrow -69x^2+224x-240=-73x^2+344x-340$

$\Rightarrow 4x^2-120x=0$

$\Rightarrow 4x(x-30)=0$

Then, $x=0$ or $x=30$