Question

State true or false:

If $\frac{x-1}{x-2}+\frac{x-3}{x-4}=3\frac{1}{3}$, then $x=5$ or $x=\frac{5}{2}$.

• A. True
• B. False

Answer 1

The correct option is A True

Given equation is, $\frac{x-1}{x-2}+\frac{x-3}{x-4}=3\frac{1}{3}$

$3(x-1)(x-4)+3(x-2)(x-3)=10(x-2)(x-4)$
$3x^2-15x+12+3x^2-15x+18=10x^2-60x+80$
$4x^2-30x+50=0$
$2x^2-15x+25=0$
$2x^2-10x-5x+25=0$
$(2x-5)(x-5)=0$
$\therefore x=5,\frac{5}{2}$