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Math Problems - Simplify Expression

by Ashley
(Orlando, Florida, United states)











































x^2-1/9x/x^2+2x+1/3x^2

what is the simplified form of


x^2-16/x+4
5/3y-2-4/9y^2-4
3x-6/x-2
5/3y-4/y^2
(x-5/x^2-3x-10)(x+2/x^2+x-12)
4z^2-4z-15/2z^2+z-15

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Aug 20, 2011
Simplify Expression
by: Staff

-----------------------------------------

Part IV



The final solutions:

A. x^2-1/9x/x^2+2x+1/3x^2

4x²/3 - 1/(9x) + 2x

Or, combined as a single fraction:

(12x³ + 18x² -1)/(9x)



B. x^2-16/x+4

No further simplification is possible. However, when all three terms are combined to form a single fraction:

(x³ + 4x - 16)/x



C. 5/3y-2-4/9y^2-4

-4y²/9 + 5y/3 - 6

Or, combined as a single fraction:

(-4y² + 15y - 54)/9



D. 3x-6/x-2

3x - 6/x - 2

No further simplification is possible. However, when all three terms are combined to form a single fraction:

(3x² - 2x - 6)/x



E. 5/3y-4/y^2

No further simplification is possible. However, when both terms are combined to form a single fraction:

(5y³ - 12)/(3y²)



F. (x-5/x^2-3x-10)(x+2/x^2+x-12)

-2(2x³ + 10x² + 5)(x³ - 6x² + 1)/x⁴

Or,

-2(2x⁶ - 2x⁵ - 60x⁴ + 7x³ - 20x² + 5)/x⁴

Or,

(-4x⁶+ 4x⁵+ 120x⁴ - 14x³ + 40x² - 10) /x⁴



G. 4z^2-4z-15/2z^2+z-15

(-7z²)/2 - 3z - 15

No further simplification is possible. However, when all three terms are combined to form a single fraction:

-(7z² + 6z + 30)/2



Thanks for writing.

Staff
www.solving-math-problems.com


Aug 20, 2011
Simplify Expression
by: Staff

-----------------------------------------

Part III


F. (x-5/x^2-3x-10)(x+2/x^2+x-12)

[(x) - (5/x²) - (3x) - (10)]*[(x) + (2/x²) + (x) - (12)]

[(x)*(x²/x²) - (5/x²) - (3x)*(x²/x²) - (10)*(x²/x²)]*[(x)*(x²/x²) + (2/x²) + (x)*(x²/x²) - (12) *(x²/x²)]

[(x³)/(x²) - (5/x²) - (3x³)/(x²) - (10x²)/(x²)]*[(x³)/(x²) + (2/x²) + (x³)/(x²) - (12x²)/(x²)]

{[(x³) - (5) - (3x³) - (10x²)]/(x²)}*{[(x³) + (2 + (x³) - (12x²)]/(x²)}

[(x³) - (5) - (3x³) - (10x²)]*[(x³) + (2) + (x³) - (12x²)]/(x²*x²)

[(x³) - (3x³) - (10x²) - (5)]*[(x³) + (x³) - (12x²)+ (2)]/(x²⁺²)

[-(2x³) - (10x²) - (5)]*[(2x³) - (12x²) + (2)]/(x⁴)

[-(2x³) - (10x²) - (5)]*[(2x³) - (12x²) + (2)]/(x⁴)

[-(2x³) - (10x²) - (5)]*[2]*[(x³) - (6x²) + (1)]/(x⁴)

2*(-2x³ - 10x² - 5)*(x³ - 6x² + 1)/x⁴

2*(-1)*(2x³ + 10x² + 5)*(x³ - 6x² + 1)/x⁴

-2(2x³ + 10x² + 5)(x³ - 6x² + 1)/x⁴

-2(2x⁶ - 2x⁵ - 60x⁴ + 7x³ - 20x² + 5)/x⁴

(-4x⁶+ 4x⁵+ 120x⁴ - 14x³ + 40x² - 10) /x⁴





G. 4z^2-4z-15/2z^2+z-15

(4z²) – (4z) - (15/2)z² + z - 15

(4z²) - (15/2)z² - (4z) + z - 15

(4z²) - (15z²/2) - (4z) + z - 15

[(4z²) - (15z²/2)] + [-(4z) + z] - 15

[(4z²) - (15z²/2)] - 3z - 15

[(4z²)*(2/2) - (15z²/2)] - 3z - 15

[(8z²)/2) - (15z²/2)] - 3z - 15

(-7z²)/2 - 3z - 15

No further simplification is possible. However, the three terms can be combined to form a single fraction.


To combine these terms as a single fraction the denominator of every term must be the same. In this case each denominator must be 2.

To accomplish this, each term must be multiplied by a fraction which will change its denominator to 2, without changing the value of the term. Therefore the numerator and the denominator of the fraction which is used in this multiplication must also be the same.

For example, if multiplying by 1/(2) will convert the denominator of a term to 2, then the actual multiplying fraction used must be (2/2).


(-7z²)/2 - (3z)*(2/2) - 15*(2/2)

(-7z²)/2 - (6z)/2) - 30/2

Since each term in the expression now has the same denominator, the numerators of the terms can be added directly.

(-7z² - 6z - 30)/2

-(7z² + 6z + 30)/2

-----------------------------------------

Aug 20, 2011
Simplify Expression
by: Staff

-----------------------------------------

Part II

C. 5/3y-2-4/9y^2-4

(5/3)y - 2 - (4/9)y² - 4

-4y²/9 + 5y/3 - 2 - 4

-4y²/9 + 5y/3 - 6

All three terms can be combined to form a single fraction.

To combine these terms as a single fraction the denominator of every term must be the same. In this case each denominator must be 9.

To accomplish this, each term must be multiplied by a fraction which will change its denominator to 9, without changing the value of the term. Therefore the numerator and the denominator of the fraction which is used in this multiplication must also be the same.

For example, if multiplying by 1/(3) will convert the denominator of a term to 9, then the actual multiplying fraction used must be (3)/(3).

(-4y²/9) + (5y/3)*(3/3) - 6*(9/9)

Since each term in the expression now has the same denominator, the numerators of the terms can be added directly.

(-4y²/9) + (15y/9) - (54/9)

(-4y² + 15y - 54)/9



D. 3x-6/x-2

3x - 6/x - 2

No further simplification is possible. However, all three terms can be combined to form a single fraction.

(3x) - (6/x) - (2)


To combine these terms as a single fraction the denominator of every term must be the same. In this case each denominator must be x.

To accomplish this, each term must be multiplied by a fraction which will change its denominator to x, without changing the value of the term. Therefore the numerator and the denominator of the fraction which is used in this multiplication must also be the same.

For example, if multiplying by 1/(x) will convert the denominator of a term to x, then the actual multiplying fraction used must be (x)/(x).

(3x)*(x/x) - (6/x) - (2)*(x/x)

(3x²)/x - 6/x - (2x)/x

Since each term in the expression now has the same denominator, the numerators of the terms can be added directly.

(3x² - 6 - 2x)/x

(3x² - 2x - 6)/x



E. 5/3y-4/y^2

(5/3)y - (4/y²)

No further simplification is possible. However, the two terms can be combined to form a single fraction.

To combine these terms as a single fraction the denominator of every term must be the same. In this case each denominator must be 3y².

To accomplish this, each term must be multiplied by a fraction which will change its denominator to 3y², without changing the value of the term. Therefore the numerator and the denominator of the fraction which is used in this multiplication must also be the same.

For example, if multiplying by 1/(y²) will convert the denominator of a term to 3y², then the actual multiplying fraction used must be (y²/y²).


(5/3)y - (4/y²)

(5y/3) - (4/y²)

(5y/3)*(y²/y²) - (4/y²)*(3/3)

(5y³)/(3y²) - (12)/(3y²)

Since each term in the expression now has the same denominator, the numerators of the terms can be added directly.

(5y³ - 12)/(3y²)

-----------------------------------------

Aug 20, 2011
Simplify Expression
by: Staff


Part I

The question:

by Ashley
(Orlando, Florida, United states)

x^2-1/9x/x^2+2x+1/3x^2

what is the simplified form of


x^2-16/x+4
5/3y-2-4/9y^2-4
3x-6/x-2
5/3y-4/y^2
(x-5/x^2-3x-10)(x+2/x^2+x-12)
4z^2-4z-15/2z^2+z-15


The answer:

A. x^2-1/9x/x^2+2x+1/3x^2

x² - (1/9)x/x² + 2x + (1/3)x²

x² + (1/3)x² - (1/9)x/x² + 2x

3x²/3 + (1/3)x² - (1/9)x/x² + 2x

(3x² + 1x²)/3 - (1/9)x/x² + 2x

4x²/3 - (1/9)x/x² + 2x

4x²/3 - (1/9)/x²⁻¹ + 2x

4x²/3 - (1/9)/x¹ + 2x

4x²/3 - (1/9)/x + 2x

4x²/3 - 1/(9x) + 2x

These three fractions can also be combined into a single fraction:

To combine these terms as a single fraction the denominator of every term must be the same. In this case each denominator must be 9x.

To accomplish this, each term must be multiplied by a fraction which will change its denominator to 9x, without changing the value of the term. Therefore the numerator and the denominator of the fraction which is used in this multiplication must also be the same.

For example, if multiplying by 1/(3x) will convert the denominator of a term to 9x, then the actual multiplying fraction used must be (3x)/(3x).

(4x²/3)*(3x)/(3x) - 1/(9x) + 2x*(9x)/(9x)

(12x³)/(9x) - 1/(9x) + (18x²)/(9x)

Since each term in the expression now has the same denominator, the numerators of the terms can be added directly.

(12x³ -1 + 18x²)/(9x)

(12x³ + 18x² -1)/(9x)



B. x^2-16/x+4

No further simplification is possible. However, all three terms can be combined to form a single fraction.

To combine these terms as a single fraction the denominator of every term must be the same. In this case each denominator must be x.

To accomplish this, each term must be multiplied by a fraction which will change its denominator to x, without changing the value of the term. Therefore the numerator and the denominator of the fraction which is used in this multiplication must also be the same.

For example, if multiplying by 1/(x) will convert the denominator of a term to x, then the actual multiplying fraction used must be (x)/(x).


x² - (16/x) + 4

(x²)*(x/x) - (16/x) + 4*(x/x)

(x³/x) - (16/x) + (4x/x)

Since each term in the expression now has the same denominator, the numerators of the terms can be added directly.

(x³ - 16 + 4x)/x

(x³ + 4x - 16)/x

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