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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

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#### Solution Preview

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 ...

#### Solution Summary

This provides several examples of simplifying rational expressions, as well as examples of finding least common multiple.

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