Question

1. Divide. (Simplify your answer completely.)

6x3y6

14a4b2

÷

36x4y3

16a9b

2. Solve. (Enter your answers as a comma-separated list.)

y + 2

y2 − y − 2

+

y + 1

y2 − 4

=

1

y + 1

3. Solve by using the quadratic formula. (Enter your answers as a comma-separated list.)

w² + 9w − 5 = 0

w =

4.

Find the coordinates of the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter DNE.)

y = x² − x − 12

(x, y) =	(smaller x-value)
(x, y) =	(larger x-value)

Answer 1

1. [(6x³ y⁶) /14a⁴ b²)] ÷ [(36x⁴y³) /(16a⁹ b)]=[(6x³ y⁶) /(14a⁴ b²)]*[(16a⁹ b)/ (36x⁴y³)]=[(6x³ y⁶)/ (36x⁴y³)] *[(16a⁹ b)/(14a⁴ b²)] = ( y³/6x)*( 8a⁵ /7b) = 4y³a⁵/21xb .

2. [(y+2)/(y²-y-2)] + [(y+1)/(y²-4)] = 1/(y+1) or, [(y+2)/(y+1)(y-2)] + [(y+1)/(y+2)(y-2)] = 1/(y+1)

or, [ (y+2)²+(y+1)²]/[(y+1)[(y-2)(y+2)]= 1/(y+1) or, [(y²+4y+4)+ (y²+2y+1)]/ [(y+1)[(y-2)(y+2)]= 1/(y+1)

or, (2y²+6y+5)/ [(y+1)[(y-2)(y+2)]= 1/(y+1) or, (2y²+6y+5)/ [(y-2)(y+2)]= 1

or, 2y²+6y+5 = y²-4 or, y²+6y+9 = 0 or, (y+3)² = 0 so that y = -3.

3. w²+9y-5= 0.

On using the quadratic formula, we get w = [ -9± √{ 9² -4*1*(-5)}]/2*1 = [ -9± √ (81+20)]/2= (-9± √101)/2.

Thus, w = -9/2 -√101/2, -9/2 +√101/2.

4. y = x²-x-12.

The x-intercepts of the given parabola are determined by equation y = 0 . Then x²-x-12.= 0 or, (x-4)(x+3) = 0.

Thus, the x-intercepts of the given parabola are ( x,y) = (-3,0)( smaller value) and ( x,y) = (4,0)( larger value) .