Question

Simplify: $\frac{(x-5)(x-3)(x^2-9x+14)}{(x^2-12x+35)(x-3)}$.

• A. $x-1$
• B. $x-2$
• C. $x-7$
• D. $(x-1)(x-2)$

Answer 1

Answer: (B)

$x-2$

$\frac{(x-5)(x-3)(x^2-9x+14)}{(x^2-12x+35)(x-3)}$ ---- ( 1 )

$\Rightarrow$ $x^2-9x+14=x^2-7x-2x+14=x(x-7)-2(x-7)=(x-7)(x-2)$ ---- ( 2 )

$\Rightarrow$ $x^2-12x+35=x^2-7x-5x+35=x(x-7)-5(x-7)=(x-5)(x-7)$ ---- ( 3 )

$\Rightarrow$ $\frac{(x-5)(x-3)(x-7)(x-2)}{(x-5)(x-7)(x-3)}$ [ Substituting equation ( 2 ) and ( 3 ) in equation ( 1 ) ]

$\Rightarrow$ $(x-2)$

$\therefore$ $\frac{(x-5)(x-3)(x^2-9x+14)}{(x^2-12x+35)(x-3)}=(x-2)$