Question

What is the quotient (4-x)/(x^2+5x-6) ÷ (x^2-11x+28)/(x^2+7x+6) in simplified form? State the restrictions on the variable.

A. (-(x+1))/((x-1)(x-7)), x≠1,x≠7
B. (-1)/((x-7)), x≠7
C. (-1)/((x-7)), x≠1,x≠-6,x≠4
D. (-(x+1))/((x-1)(x-7)), x≠1,x≠-6,x≠4,x≠7

Answer 1

(4-x)/(x+6)(x-1)÷(x-7)(x-4)/(x+1)(x+6)=(4-x)/(x+6)(x-1) x (x+1)(x+6)/(x-7)(x-4)=
-1(x-1)/(x-1)(x-7)=-1/(x-7), x cannot be 7. ☺☺☺☺

Answer 2

Answer with explanation:

The Expression which we have to write in Simplified form is :

`((4-x)/(x^2+5 x -6))/((x^2-11x+28)/(x^2+7x+6))\\\\=(4-x)/(x^2+6 x-x-6) * (x^2+6 x +x+6)/(x^2-7 x-4 x+28)\\\\= (4-x)/(x*(x+6)-1*(x+6)) * (x*(x+6)+1 *(x+6))/(x*(x-7)-4*(x-7))\\\\= (4-x)/((x-1)(x+6))* ((x+1)(x+6))/((x-4)(x-7))\\\\ \text{Cancelling ,(x+6) and (x-4),from numerator and Denominator}\\\\=(-1* (x+1))/((x-1)(x-7))`

Option A