Lyle
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Given
Fraction 1: (x^2-16)/(2x^2-9x+4)
Fraction 2: (2x^2+14x+24)/(4x+4)
Fraction 1 divided by Fraction 2:
(x^2-16)/(2x^2-9x+4) ÷ (2x^2+14x+24) ÷ (4x+4)
(x^2-16)/(2x^2-9x+4) (2x^2+14x+24) ÷ (4x+4) (4x+4)
(2x^2-x^2+2x^2-9x+16)/(3x^2+2x^2-9x+36) (-2x+14) ÷ (-2x+2)
5x-3/6x^2+5x-39
Multiply both the numerator and denominator by 3:
(15x-9)/(18x^2+9x-117)
Divide both the numerator and denominator by x+3:
(15x-9)/(18x^2+9x-117) ÷ x+3
(15-9) ÷ (18(x^2-9)) ÷ (x+3)
6 ÷ (-9x+36) ÷ (x+3)
6 ÷ (-9x+36+x-3)
= 6 ÷ 33 = 2/11
Therefore, Fraction 1 divided by Fraction 2 is equal to 2/11 or 0.181818 repeating.
Option B, The quantity 2 times x plus 2 over the quantity x plus 3 is incorrect because it has both numerator and denominator in terms of x only
What is the quotient Fraction 1: the quantity x squared minus 16 over the quantity 2 times x squared minus 9 times x plus 4; Fraction 2: the quantity 2 times x squared plus 14 times x plus 24 over the quantity 4 times x plus 4; Find Fraction 1 divided by Fraction 2. ?
A. 1 over the quantity x plus 3
B. The quantity 2 times x plus 2 over the quantity x plus 3
C. The quantity 2 times x plus 2 over the quantity 2 times x squared plus 5 times x minus 3
D. 2 times the quantity x plus 1 over the quantity 2 times x squared minus 5 times x minus 3
4 answers
Option C, The quantity 2 times x plus 2 over the quantity 2 times x squared plus 5 times x minus 3 is incorrect because it has a squared variable.
Option D, 2 times the quantity x plus 1 over the quantity 2 times x squared minus 5 times x minus 3 is incorrect because it has a squared variable.
Option D, 2 times the quantity x plus 1 over the quantity 2 times x squared minus 5 times x minus 3 is incorrect because it has a squared variable.
What is the quotient Fraction 1: the quantity x squared minus 16 over the quantity 2 times x squared minus 9 times x plus 4; Fraction 2: the quantity 2 times x squared plus 14 times x plus 24 over the quantity 4 times x plus 4; Find Fraction 1 divided by Fraction 2. ?
A. 1 over the quantity x plus 3
B. The quantity 2 times x plus 2 over the quantity x plus 3
C. The quantity 2 times x plus 2 over the quantity 2 times x squared plus 5 times x minus 3
D. 2 times the quantity x plus 1 over the quantity 2 times x squared minus 5 times x minus 3
A. 1 over the quantity x plus 3
B. The quantity 2 times x plus 2 over the quantity x plus 3
C. The quantity 2 times x plus 2 over the quantity 2 times x squared plus 5 times x minus 3
D. 2 times the quantity x plus 1 over the quantity 2 times x squared minus 5 times x minus 3
The correct answer is B. The quantity 2 times x plus 2 over the quantity x plus 3.
To get to this answer, we first need to simplify both fractions:
Fraction 1: (x^2-16)/(2x^2-9x+4) can be factored as (x+4)(x-4)/(2x-1)(x-4)
Fraction 2: (2x^2+14x+24)/(4x+4) can be simplified as 2(x^2+7x+12)/4(x+1)
We can now rewrite the division of Fraction 1 by Fraction 2 as the product of Fraction 1 by the reciprocal of Fraction 2:
((x+4)(x-4)/(2x-1)(x-4)) / (2(x^2+7x+12)/4(x+1))
Simplifying the expression by cancelling out (x-4) and then simplifying common terms:
((x+4)/(2x-1)) * ((x+1)/ (x^2+7x+12)) = (x+4)(x+1) / (2x-1)(x+3)
This expression can be further simplified as (x+4)(x+1)/(2x-1)(x+3) = (2x+2)/(x+3) = 2(x+1)/(x+3), which matches answer B.
To get to this answer, we first need to simplify both fractions:
Fraction 1: (x^2-16)/(2x^2-9x+4) can be factored as (x+4)(x-4)/(2x-1)(x-4)
Fraction 2: (2x^2+14x+24)/(4x+4) can be simplified as 2(x^2+7x+12)/4(x+1)
We can now rewrite the division of Fraction 1 by Fraction 2 as the product of Fraction 1 by the reciprocal of Fraction 2:
((x+4)(x-4)/(2x-1)(x-4)) / (2(x^2+7x+12)/4(x+1))
Simplifying the expression by cancelling out (x-4) and then simplifying common terms:
((x+4)/(2x-1)) * ((x+1)/ (x^2+7x+12)) = (x+4)(x+1) / (2x-1)(x+3)
This expression can be further simplified as (x+4)(x+1)/(2x-1)(x+3) = (2x+2)/(x+3) = 2(x+1)/(x+3), which matches answer B.