Question

Solve: $\frac{3}{x-1}+\frac{4}{x-2}=\frac{7}{x-3}$

• A. $2\frac{3}{5}$
• B. $9\frac{3}{5}$
• C. $3\frac{3}{5}$
• D. $1\frac{3}{5}$

Answer 1

The correct option is D $1\frac{3}{5}$

$\frac{3}{x-1}+\frac{4}{x-2}=\frac{7}{x-3}$
$=>\frac{3}{x-1}+\frac{4}{x-2}-\frac{7}{x-3}=0$
$=>\frac{3(x-2)(x-3)+4(x-1)(x-3)-7(x-1)(x-2)}{(x-1)(x-2)(x-3)}=0$
$=>3(x^2-3x-2x+6)+4(x^2-3x-x+3)-7(x^2-2x-x+2)=0$
$=>3x^2-9x-6x+18+4x^2-12x-4x+12-7x^2+14x+7x-14=0$
$=>-10x=-16$
$=>x=\frac{16}{10}$
$=>x=\frac{8}{5}$
$=>x=1\frac{3}{5}$