Question

Solve: $\frac{5}{x-2}+\frac{1}{x-1}=\frac{6}{x};x\ne 0,1,2$.

• A. $\frac{13}{11}$
• B. $\frac{12}{11}$
• C. $\frac{17}{11}$
• D. $\frac{16}{11}$

Answer 1

The correct option is B $\frac{12}{11}$

$\frac{5}{x-2}+\frac{1}{x-1}=\frac{6}{x}$

$=>\frac{5(x-1)+(x-2)}{(x-2)(x-1)}=\frac{6}{x}$

$=>(5x-5+x-2)\left(x\right)=(x^2-x-2x+2)\left(6\right)$

$=>5x^2-5x+x^2-2x=6x^2-6x-12x+12$

$=>-7x+18x=12$

$=>11x=12$

$=>x=\frac{12}{11}$