What is the simplified form of left parenthesis x squared times yz right parenthesis squared left parenthesis x y squared z squared right parenthesis over left parenthesis xyz right parenthesis squared ?
(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:
The simplified form of the given expression is:
start fraction (xyz)^2(xyz) over x end fraction
or
\(\frac{{(xyz)^2(xyz)}}{x}\)
What is the excluded value of the rational expression start fraction 2x plus 6 over 4x minus 8 end fraction ?
(1 point)
Responses
Image with alt text:
Image with alt text:
0
0
2
To find the excluded value, we need to identify the value(s) of x that would make the denominator equal to zero. In this case, the denominator is 4x - 8.
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.
What is the simplified form of start fraction x squared minus 25 over x squared minus 3x minus 10 end fraction ?
(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
The simplified form of the given rational expression is:
start fraction (x - 5)(x + 5) over (x + 2)(x - 3) end fraction
or
\(\frac{{(x - 5)(x + 5)}}{{(x + 2)(x - 3)}}\)
Multiple Choice
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
To find the quotient Fraction 1 divided by Fraction 2, we need to multiply Fraction 1 by the reciprocal of Fraction 2.
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.
1 over the quantity x plus 3Image 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
Image with alt text: 2 times the quantity x plus 1 over the quantity 2 times x squared minus 5 times x minus 3
To find the quotient Fraction 1 divided by Fraction 2, we need to multiply Fraction 1 by the reciprocal of Fraction 2.
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
What is the simplified form for the product Fraction 1: the quantity x plus 1 over the quantity x squared minus 25; Fraction 2: the quantity x plus 5 over the quantity x squared plus 8 times x plus 7; Find Fraction 1 times by Fraction 2.?
(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