Adding and subtracting radical equations, homework help

Find the LCM of the polynomials.

2x – 4, 5x – 10

10×2 – 40x + 40

10x – 20

10×2 – 40

10×2 + 40

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Find the LCM of the polynomials.

4x2y4, 10xyz

20x2y4z

40x3y5z

20xyz

20x2y4

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Add the rational expressions and simplify.

$fraction numerator 5 over denominator 6 y end fraction plus fraction numerator 1 over denominator 8 z end fraction$

A. $fraction numerator 6 over denominator 6 y space plus space 8 z end fraction$

B. $fraction numerator 3 over denominator 3 y space plus thin space 4 z end fraction$

C. $fraction numerator 1 over denominator 8 z y end fraction$

D. $fraction numerator 20 z space plus space 3 y over denominator 24 z y end fraction$

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Add the rational expressions and simplify.

$fraction numerator 5 over denominator x squared space minus space 3 x space minus space 28 end fraction space plus space fraction numerator 2 over denominator 2 x space minus space 14 end fraction$

A. $fraction numerator x space plus space 9 over denominator x squared space minus space 3 x space minus space 28 end fraction$

B. $fraction numerator x space plus thin space 14 over denominator 2 x squared space minus space 6 x space minus space 56 end fraction$

C. $fraction numerator x space plus space 10 over denominator x squared space minus space 3 x space minus space 28 end fraction$

D. $fraction numerator 2 x space plus space 28 over denominator 2 x squared space minus space 6 x space minus space 56 end fraction$

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Subtract the rational expressions and simplify.

$fraction numerator a over denominator a space minus space 4 end fraction space minus space fraction numerator 3 over denominator 4 space minus space a end fraction$

A. $fraction numerator 3 space minus space a over denominator 4 space minus space a end fraction$

B. $fraction numerator negative a space minus space 3 over denominator 4 space minus space a end fraction$

C. $fraction numerator a space minus space 3 over denominator a space minus space 4 end fraction$

D. $fraction numerator negative a space plus thin space 3 over denominator 4 space minus space a end fraction$

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Subtract the rational expressions and simplify.

$fraction numerator x over denominator x squared space plus space 5 x space plus thin space 6 end fraction space minus space fraction numerator 2 over denominator x squared space minus space 9 end fraction$

A. $fraction numerator x squared space minus space 5 x space plus space 4 over denominator x cubed space plus thin space 2 x squared space minus space 9 x space minus space 18 end fraction$

B. $fraction numerator x space minus space 2 over denominator 5 x space minus space 3 end fraction$

C. $fraction numerator x squared space minus space 5 x space minus space 4 over denominator x cubed space plus thin space 2 x squared space minus space 9 x space minus space 18 end fraction$

D. $fraction numerator x space minus space 2 over denominator 5 x space plus space 15 end fraction$

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Simplify the complex fraction completely.

$fraction numerator left parenthesis a space plus space b right parenthesis left parenthesis begin display style 1 over a end style space minus space begin display style 1 over b end style right parenthesis over denominator left parenthesis a space minus space b right parenthesis left parenthesis begin display style 1 over a end style space plus space begin display style 1 over b end style right parenthesis end fraction$

A. $fraction numerator b space minus space a over denominator a space minus space b end fraction$

C. $fraction numerator left parenthesis a squared b space plus space a b squared right parenthesis left parenthesis b space minus space a right parenthesis over denominator left parenthesis a squared b space minus space a b squared right parenthesis left parenthesis b space plus space a right parenthesis end fraction$

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Simplify the expression.

$fraction numerator m squared space plus space n squared over denominator m squared space minus space n squared end fraction thin space plus space fraction numerator m over denominator n space minus space m end fraction space plus space fraction numerator n over denominator m space plus space n end fraction$

A. $fraction numerator 2 m squared space plus space 2 m n space plus space 2 n squared over denominator m squared space minus space n squared end fraction$

B. $fraction numerator 2 m squared space plus space 2 m n over denominator m squared space minus space n squared end fraction$

C. $fraction numerator 2 m n over denominator m squared space minus space n squared end fraction$

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What is the sum of $fraction numerator x space minus space y over denominator 5 end fraction$ and $fraction numerator x space plus space y over denominator 4 end fraction$ ?

A. $fraction numerator x space plus space 9 y over denominator 20 end fraction$

B. $fraction numerator 9 x space plus space y over denominator 20 end fraction$

C. $fraction numerator 9 x space minus space y over denominator 20 end fraction$

D. $fraction numerator x space minus space 9 y over denominator 20 end fraction$

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Find the perimeter of the quadrilateral below. Write in simplest form.

A. $fraction numerator 27 x squared space plus space 40 x space minus space 8 over denominator 5 x cubed space minus space 20 x end fraction$

B. $fraction numerator 17 over denominator x squared space plus space 7 x space minus space 4 end fraction$

C. $fraction numerator 77 x cubed space minus space 118 x squared space minus space 168 x space plus thin space 32 over denominator 5 x to the power of 4 space minus space 20 x cubed space minus space 20 x squared space plus space 80 x end fraction$