Question

What is the quotient in simplified form? State any restrictions on the variable? \frac{x^2-16}{x^2+5x+6} /\frac{x^2+5x+4}{x^2-2x-8}

Answer 1

`(x^2-16)/(x^2+5x+6) / (x^2+5x+4)/(x^2-2x-8)`

We can begin by rearranging this into multiplication:


`(x^2-16)/(x^2+5x+6) * (x^2-2x-8)/(x^2+5x+4)`

Now we can factor the numerators and denominators:


`((x+4)(x-4))/((x+3)(x+2)) * ((x-4)(x+2))/((x+4)(x+1))`

The factors (x+4) and (x+2) cancel out, leaving us with:


`((x-4))/((x+3)) * ((x-4))/((x+1))`

Our answer comes out to be:


`((x-4)^(2) )/((x+3)(x+1))` or
`( x^(2) -8x+16)/( x^(2)+4x+3 )`

Based on the numerator of the second fraction (since we used its inverse), the denominators of both, and the factors we canceled out earlier, the restrictions are x ≠ -4, -3, -2, -1, 4

Answer 2

Full...Solving Rational Equations Quiz part 1.

1.c. n^2-6/n^2-2 ; n = +/- sqrt5, n= +/- sqrt2

2.B. 4a/7b^2 , a = 0, b = 0

3.C. (x-4)^2/(x+3)(x+1) ; x= -4,-3,-2,-1,4

4.B. (x+1)(x-1)(x^2+1)

5.A. 7a-49/(a-8)(a+8)

6.A. 21a-28/(A-6)(a+8)

7.C. 4x/3x^2+10x+3

8.C. 3x^2(y+4)/7y

9.D. -11/3

10.D. 14

11. D. 9 mi/h downstream, 6 mi/h upstream

Explanation:

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