Reducing Algebraic Fractions Worksheet

Algebraic fractions can sometimes be a daunting subject for students. However, with the right practice and understanding, they can become much easier to work with. If you're a student looking to improve your skills in reducing algebraic fractions, you've come to the right place. In this worksheet, we will provide you with a set of practice problems that will help you master the art of simplifying algebraic fractions.

  Equivalent Fractions Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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  Two-Step Equations Worksheet

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Determine the simplified form of the fraction 12x^3 / 6x^2.

The simplified form of the fraction 12x^3 / 6x^2 is 2x.

Simplify the expression (3x^2 - 6x) / (9x^3 - 18x^2).

To simplify the expression (3x^2 - 6x) / (9x^3 - 18x^2), we can first factor out a 3x from the numerator and a 9x^2 from the denominator to get (3x(x - 2)) / (9x^2(x - 2)). Now, we can cancel out the common factors of x - 2 to simplify the expression to 3x / 9x^2, which simplifies to 1 / 3x. Thus, the simplified expression is 1 / 3x.

Reduce the fraction (4y^4 + 8y) / (2y^2).

The fraction (4y^4 + 8y) / (2y^2) can be simplified by dividing each term in the numerator by the denominator. This simplifies to 2y^2 + 4.

Find the simplest form of (2x^3 + 4x^2) / (x^2 - 2x).

The simplest form of (2x^3 + 4x^2) / (x^2 - 2x) is 2x.

Simplify the following expression: (6a^2b^3 + 9ab^2) / (3ab + 6a^2).

To simplify the expression (6a^2b^3 + 9ab^2) / (3ab + 6a^2), factor out a common term from the numerator and the denominator, you get 3ab(2ab^2 + 3b) / 3a(b + 2a), then cancel out the common terms in the numerator and the denominator, you end up with 2b^2 / (b + 2a).

Reduce the fraction (5x^4 - 15x^2 + 10x) / (2x^3 - 4x^2 + 6x).

To reduce the fraction (5x^4 - 15x^2 + 10x) / (2x^3 - 4x^2 + 6x), you can simplify by factoring out the greatest common factor in the numerator and the denominator. The greatest common factor is 5x. Factoring out 5x, you get 5x(x^3 - 3x + 2) / 2x(x^2 - 2x + 3). You can then simplify further by canceling out the common factor 5x in the numerator and denominator, resulting in (x^3 - 3x + 2) / 2(x^2 - 2x + 3) as the reduced form of the fraction.

Find the simplest form of (7y^3 - 21y^2 + 14y) / (35y^2 - 49).

To simplify the expression (7y^3 - 21y^2 + 14y) / (35y^2 - 49), we can first factor both the numerator and denominator. Factoring out common factors from the numerator, we get 7y(y^2 - 3y + 2), and from the denominator we have 7(5y + 7)(5y - 7). Canceling out the common factor of 7, we are left with (y^2 - 3y + 2) / (5y + 7)(5y - 7) as the simplest form of the expression.

Simplify the expression (8x^3 + 12x^2) / (4x).

The expression simplifies to 2x^2 + 3x.

Reduce the fraction (6a^5 + 9a^3) / (3a).

To reduce the fraction (6a^5 + 9a^3) / (3a), we first factor out the common term, 3a, from the numerator which gives us 3a(2a^4 + 3a^2). So, the reduced fraction is 2a^4 + 3a^2.

Find the simplest form of (3x^2 + 6x) / (9x^3 - 12x^2 + 15x).

To find the simplest form of (3x^2 + 6x) / (9x^3 - 12x^2 + 15x), we can first factor out a common factor from the numerator and denominator, which is x. This simplifies the expression to x(3x + 6) / x(9x^2 - 12x + 15). The x terms cancel out, leaving us with (3x + 6) / (9x^2 - 12x + 15). Now, we can simplify further by dividing all terms by 3, resulting in (x + 2) / (3x^2 - 4x + 5) as the simplest form of the expression.