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    Rational expressions and least common multiple

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    Find all numbers for which the rational expression is undefined.
    -15/23z

    Find all numbers for which the rational expression is undefined.
    (t^(3 )-6t)/(t^2-25)

    Simplify by removing factor of 1.
    (〖80v〗^( 8 ) y^9)/(〖50v〗^(4 ) y^6 ) (The simplified form is)

    Simplify by removing factor of 1.
    (r^(2 )-16)/(r^(2 )-8r+16)

    Simplify by removing factor of 1
    (〖21v〗^(2 )-189)/(〖49v〗^(2 )-441)

    Multiply and simplify
    〖7b〗^(7 )/〖11v〗^4 ∙ 〖121v〗^8/49b

    Multiply and simplify
    (w^(2 )-4w-45)/(w^(2 )-10w+25 ) ∙ (w-5)/(w-9) (Simplify your answer)

    Divide and simplify
    f/b^2 ÷ f^2/b^3

    Divide and simplify
    (x^(2 )-36)/x ÷ (x-6)/(x+7) (Type a fraction. Leave your answer in factored form)

    Divide and simplify
    (x^(2 )-1)/(49x+49) ÷ (x-1)/7 (Type a fraction)

    Divide and simplify
    (z^(2 )+4z)/(z^(2 )+2z-8) ÷ z/(z+2) (Type a fraction)

    Find the LCM of
    〖10x〗^4, 〖50x〗^6

    Find the LCM of
    q^(2 )-49,q^(2 )+12q+35

    Find the LCM of
    w^(3 )+ 〖10w〗^(2 )+25w, w^(2 )-10w

    〖9y〗^2+45y,〖 3y〗^2+24y+45

    Add
    6/(8+z) +1/(8+z)

    Add. Simplify if possible
    (x^(2 )+13x)/(x^(2 )-8x) +(x^(2 )-6x)/(x^(2 )-8x)

    Add. Simplify if possible
    7/〖25z〗^3 +1/〖35z〗^2

    Add.
    6/(v-8) +6/(v-8) (Simplify your answer)

    Add. Simplify if possible
    6x/(x^(2 )-9) +x/(x-3)

    Add and simplify if possible
    (w+1)/w +w/(w+1)

    Subtract and simplify if possible
    (z-9)/z-(3z-17)/7z (Simplify your answer. Use integers or fraction for any numbers in the expression)

    3/(〖7s〗^(2 )-7s) -7/(7s-7) ((Simplify your answer. Use integers or fraction for any numbers in the expression)

    Subtract. Simplify by removing a factor of 1 when possible
    12bc/b^(2 -c^2 ) - (b-c)/(b+c)

    Subtract. Simplify if possible
    (4-z)/(z-2)-(2z-5)/(2-z) (Simplify your answer)

    Perform the indicated operation and simplify
    (x-2)/(x-4)-(x+1)/(x+4)+(x-20)/(x^(2 )-16)

    Simplifying the expression
    (a²-1)/(a-1)-a

    Simplify
    ((x^2 - 1) / (x - 1)) - 1

    © BrainMass Inc. brainmass.com December 24, 2021, 7:41 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/rational-expressions-least-common-multiple-210429

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    SOLUTION This solution is FREE courtesy of BrainMass!

    Please see the attached file for detailed solution.

    1. Find all numbers for which the rational expression is undefined.

    The denominator cannot be zero, so

    Thus, the expression is undefined at 0.

    2. Find all numbers for which the rational expression is undefined.

    The denominator cannot be zero, so first find out the values that make the denominator 0, then we can exclude those values from the expression:

    Thus, the expression is undefined at -5 and 5.

    3. Simplify by removing factor of 1.
    (The simplified form is)

    The property of the exponents we used in above simplification is

    4. Simplify by removing factor of 1.

    We first factor the numerator using the difference of squares formula and the denominator by perfect square formula, then cancel out the common factors in the numerator and denominator:

    5. Simplify by removing factor of 1

    First factor the numerator and denominator by extracting out the greatest common factor (GCF) separately , and then cancel out the common factors in the numerator and denominator:

    6. Multiply and simplify

    7. Multiply and simplify
    (Simplify your answer)
    Factor the trinomials first:
    By grouping,
    By perfect square formula:

    Then cancel out the common factors in the numerator and denominator:

    8. Divide and simplify

    Flip the numerator and the denominator of the second fraction to convert the division to multiplication, then simplify:

    9. Divide and simplify
    (Type a fraction. Leave your answer in factored form)

    Difference of squares formula:

    10. Divide and simplify
    (Type a fraction)

    11. Divide and simplify
    (Type a fraction)
    Factor by extracting out the GCF z:
    Factor the trinomial by grouping:

    Flip the numerator and the denominator of the second fraction to convert the division to multiplication, then simplify:

    12. Find the LCM of
    ,
    The LCM of 10 and 50 is 50
    The LCM of x4 and x6 is x6
    So the LCM of 10x4 and 50x6 is 50x6.

    13. Find the LCM of

    Factor the two expressions:

    The LCM is the product of all factors:

    14. Find the LCM of
    +

    Then the LCM is

    15.

    The LCM of 3 and 9 is 9.
    So the LCM is

    From No. 16 to No. 28, the concepts are:
    (a) factor the denominators if possible
    (b) find the LCD (least common denominator)
    (c) write the fractions using the LCD as denominators
    (d) perform the necessary operations (add or subtract the numerators)
    (e) simplify the final single fraction if possible

    16. Add

    Since they already have a common denominator, we just add the numerator together:

    17. Add. Simplify if possible

    Again, they already have a common denominator, so we just add the numerator together:

    18. Add. Simplify if possible

    The LCM of 25 and 35:
    25 = 5 * 5
    35 = 5 * 7
    So LCM is 5 * 5 * 7 = 175
    The LCM of z2 and z3 is z3.
    Therefore, the LCD is 175z3.
    First write the fractions using the LCD as the denominators, and then simplify:

    19. Add.
    (Simplify your answer)

    20. Add. Simplify if possible

    Factor the denominator in the first fraction:

    The second denominator is (x - 3)
    So the LCD is (x -3)(x + 3)
    Thus

    21. Add and simplify if possible

    The LCD is w(w +1)
    So

    22. Subtract and simplify if possible
    (Simplify your answer. Use integers or fraction for any numbers in the expression)

    23. ((Simplify your answer. Use integers or fraction for any numbers in the expression)

    24. Subtract. Simplify by removing a factor of 1 when possible

    After factoring out the denominator, there is no common factors in the numerator and the denominator.

    25. Subtract. Simplify if possible
    (Simplify your answer)

    26. Perform the indicated operation and simplify

    The last denominator can be factored as x2 - 16 = (x - 4)(x + 4)
    So the LCD is (x - 4)(x + 4), then

    27. Simplifying the expression
    (a²-1)/(a-1)-a

    28. Simplify
    ((x^2 - 1) / (x - 1)) - 1

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:41 pm ad1c9bdddf>
    https://brainmass.com/math/basic-algebra/rational-expressions-least-common-multiple-210429

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