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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

Respuesta :

jorel1380
(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 with explanation:

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

[tex]\frac{\frac{4-x}{x^2+5 x -6}}{\frac{x^2-11x+28}{x^2+7x+6}}\\\\=\frac{4-x}{x^2+6 x-x-6} \times \frac{x^2+6 x +x+6}{x^2-7 x-4 x+28}\\\\= \frac{4-x}{x\times(x+6)-1\times(x+6)} \times \frac{x\times(x+6)+1 \times(x+6)}{x\times(x-7)-4\times(x-7)}\\\\= \frac{4-x}{(x-1)(x+6)}\times \frac{(x+1)(x+6)}{(x-4)(x-7)}\\\\ \text{Cancelling ,(x+6) and (x-4),from numerator and Denominator}\\\\=\frac{-1\times (x+1)}{(x-1)(x-7)}[/tex]

Option A

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