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

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

hope helped

Answer 2

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