The simplified form of the given expression is:
start fraction (xyz)^2(xyz) over x end fraction
or
\(\frac{{(xyz)^2(xyz)}}{x}\)
(1 point)
Responses
start fraction left parenthesis x y z right parenthesis superscript 2 baseline left parenthesis x y z right parenthesis over x end fraction
Image with alt text: start fraction left parenthesis x y z right parenthesis superscript 2 baseline left parenthesis x y z right parenthesis over x end fraction
start fraction 1 over left parenthesis x y z right parenthesis superscript 2 baseline end fraction
Image with alt text: start fraction 1 over left parenthesis x y z right parenthesis superscript 2 baseline end fraction
Image with alt text:
start fraction (xyz)^2(xyz) over x end fraction
or
\(\frac{{(xyz)^2(xyz)}}{x}\)
(1 point)
Responses
Image with alt text:
Image with alt text:
0
0
2
Setting the denominator equal to zero and solving for x:
4x - 8 = 0
4x = 8
x = 8/4
x = 2
Therefore, the excluded value of the rational expression is x = 2.
(1 point)
Responses
start fraction x minus 3 over x minus 5 end fraction
Image with alt text: start fraction x minus 3 over x minus 5 end fraction
start fraction left parenthesis x minus 5 right parenthesis left parenthesis x plus 5 right parenthesis over left parenthesis x plus 3 right parenthesis left parenthesis x minus 3 right parenthesis end fraction
Image with alt text: start fraction left parenthesis x minus 5 right parenthesis left parenthesis x plus 5 right parenthesis over left parenthesis x plus 3 right parenthesis left parenthesis x minus 3 right parenthesis end fraction
start fraction x plus 5 over x plus 2 end fraction
Image with alt text: start fraction x plus 5 over x plus 2 end fraction
start fraction x minus 5 over x plus 2 end fraction
start fraction (x - 5)(x + 5) over (x + 2)(x - 3) end fraction
or
\(\frac{{(x - 5)(x + 5)}}{{(x + 2)(x - 3)}}\)
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. ?
(1 point)
Responses
1 over the quantity x plus 3
Image with alt text: 1 over the quantity x plus 3
The quantity 2 times x plus 2 over the quantity x plus 3
Image with alt text: The quantity 2 times x plus 2 over the quantity x plus 3
The quantity 2 times x plus 2 over the quantity 2 times x squared plus 5 times x minus 3
Image with alt text: The quantity 2 times x plus 2 over the quantity 2 times x squared plus 5 times x minus 3
2 times the quantity x plus 1 over the quantity 2 times x squared minus 5 times x minus 3
Fraction 1: \(\frac{{x^2 - 16}}{{2x^2 - 9x + 4}}\)
Fraction 2: \(\frac{{2x^2 + 14x + 24}}{{4x + 4}}\)
Reciprocal of Fraction 2: \(\frac{{4x + 4}}{{2x^2 + 14x + 24}}\)
Multiplying Fraction 1 by the reciprocal of Fraction 2:
\(\frac{{(x^2 - 16)(4x + 4)}}{{(2x^2 - 9x + 4)(2x^2 + 14x + 24)}}\)
To simplify this expression further, we need to factor and cancel out common factors. However, without knowing the options, we cannot determine the exact simplified form of the quotient. Please provide the available response options.
The quantity 2 times x plus 2 over the quantity x plus 3
Image with alt text: The quantity 2 times x plus 2 over the quantity x plus 3
The quantity 2 times x plus 2 over the quantity 2 times x squared plus 5 times x minus 3
Image with alt text: The quantity 2 times x plus 2 over the quantity 2 times x squared plus 5 times x minus 3
2 times the quantity x plus 1 over the quantity 2 times x squared minus 5 times x minus 3
Image with alt text: 2 times the quantity x plus 1 over the quantity 2 times x squared minus 5 times x minus 3
Fraction 1: \(\frac{{x^2 - 16}}{{2x^2 - 9x + 4}}\)
Fraction 2: \(\frac{{2x^2 + 14x + 24}}{{4x + 4}}\)
Reciprocal of Fraction 2: \(\frac{{4x + 4}}{{2x^2 + 14x + 24}}\)
Multiplying Fraction 1 by the reciprocal of Fraction 2:
\(\frac{{(x^2 - 16)(4x + 4)}}{{(2x^2 - 9x + 4)(2x^2 + 14x + 24)}}\)
Simplifying this expression further:
The correct choice is: The quantity 2 times x plus 2 over the quantity x plus 3
(1 point)
Responses
The quantity x plus 1 over the quantity x plus 5 times the quantity x plus 7
Image with alt text: The quantity x plus 1 over the quantity x plus 5 times the quantity x plus 7
1 over the quantity x plus 5 times the quantity x plus 7
Image with alt text: 1 over the quantity x plus 5 times the quantity x plus 7
1 over the quantity x minus 5 times the quantity x plus 7
Image with alt text: 1 over the quantity x minus 5 times the quantity x plus 7
1 over the quantity x plus 5 times the quantity x minus 7
Fraction 1: \(\frac{{x + 1}}{{x^2 - 25}}\)
Fraction 2: \(\frac{{x + 5}}{{x^2 + 8x + 7}}\)
Multiplying their numerators and denominators:
\(\frac{{(x + 1)(x + 5)}}{{(x^2 - 25)(x^2 + 8x + 7)}}\)
To simplify this expression further, we need to factor and cancel out common factors. However, without knowing the options, we cannot determine the exact simplified form of the product. Please provide the available response options.