Abeka algebra 1 quiz 34

#10 x-5/2x² ÷ x-5/6x

first, multiply by the reciprocal: = x-5/2x² * 6x/x-5 = x-5/2x² * 2*3x/(x-5) → cancel everything that you can and whatever is left is the answer to the first part of the question. = 3/x where x≠5

questions #4-5: indicate the value(s) at which each expression is undefined. #4 x²+6x+5/x+2

x+2=0 x=-2

#5 x+2x+1/x²-25

x²-25=0 (x+5)(x-5)=0 x+5=0 x-5=0 x=-5 x=5 x=±5

#7 rs

1/rs

#3 x²+12/x²-16 (x=-4)

= (-4)²+12/(-4)²-16 = 16+12/16-16 = 28/0 → undefined

#9 x+1/x-5 * (x²-6x+5)/(x²+8x+7)

= (x+1)/(x-5) * (x-1)(x-5)/(x+1)(x+7) → cancel everything that you can and whatever is left is the answer to the first part of the question. =x-1/x+7 where x≠-1, 5

questions #8-10: multiply or divide rational expressions as indicated; write the resulting expression in reduced factored form then indicate the excluded values of x. #8 2(x+2)/4x² * 10x/x²-4

= 2(x+2)/2*2x² * 2*5x/(x+2)(x-2) → cancel everything that you can and whatever is left is the answer to the first part of the question. = 5/x(x-2) where x≠-2

questions #1-3: evaluate each rational expression at the given value(s); if the resulting value is undefined, write undefined. #1 3yz³/5x² (x=2; y=5; z=1)

= 3(5)(1)³/5(2)² = 15/5(4) = 15/20 = 3/4

#2 8y-2/x²+6 (x=3; y=-3)

= 8(-3)-2/(3)²+6 = -24-2/9+6 = -26/15 or -1 11/15

questions #6-7: write the reciprocal of each rational expression. #6 2a²/bc

bc/2a²