Question

Simplify the rational expression. x−6/x^2−7x+6
A. x/x+1
B. 1/x−1
C. x−1/x+1
D. x/x

Factor out the common binomial in the expression. 12(x-5) + 7x(x-5)
A. (x-5)(12+7x)
B. (7x-5)(12+x)
C. 2(x-5)(12+x)
D. (x+5)(12-7x)

Answer 1

$\dfrac{x-6}{x^2-7x+6}=\dfrac{x-6}{x^2-x-6x+6}=\dfrac{x-6}{x(x-1)-6(x-1)}\\\\=\dfrac{x-6}{(x-1)(x-6)}=\dfrac{1}{x-1}\to\fbox{B.}\\\\\\12(x-5)+7x(x-5)=(x-5)(12+7x)\to\fbox{A.}$

Answer 2

     (x-6)               (x-6)
--------------- = ----------------- = 1/(x-1)  so choice B. is right sure 
x^2 -7x +6         (x-6)(x-1)

hope helped