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

What is the quotient (4-x)/(x^2+5x-6) divided (x^2 - 11x + 28) / (x^2 + 7x +6) in-example-1
User LekoArts
by
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1 Answer

3 votes

Step-by-step explanation:

To solve the question, we will have to get the factor of the terms given

Let us follow the steps below

Step 1: Write out the given expression


(4-x)/(x^2+5x-6)/(x^2-11x+28)/(x^2+7x+6)

Step 2: simplify each term by writing them in factor form


(4-x)/((x-1)(x+6))/((x-4)(x-7))/((x+1)(x+6))

Step 3: Re-write the expression


(4-x)/((x-1)(x+6))*((x+1)(x+6))/((x-4)(x-7))

Step 4: Simplify further and cancel out like terms


(4-x)/(x-1)*(x+1)/((x-4)(x-7))

Step 5: simplify by factoring out the negative sign


(-(x-4))/(x-1)*(x+1)/((x-4)(x-7))

Step 6: Resolve the expression


(-1(x+1))/((x-1)(x-7))

Thus, we have the simplified form to be


(-x-1)/((x-1)(x-7))

Then for the restrictions, these will be values of x which makes it undefined

These values are


x=1\text{ and x=7}

User Jennise
by
7.4k points
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