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# Solving Fractional Equations Common Core Algebra 2 Homework

## Solving Fractional Equations Common Core Algebra 2 Homework

Fractional equations are equations that contain fractions with variables in the numerator or denominator. Solving fractional equations involves finding the value of the variable that makes the equation true. In this article, we will review some methods and examples of solving fractional equations that are aligned with the Common Core Algebra 2 standards.

## Cross-Product Method

The cross-product method is a technique that can be used to solve fractional equations by eliminating the fractions. The cross-product method is based on the property that if two fractions are equal, then their cross-products are also equal. For example, if a/b = c/d, then ad = bc.

To use the cross-product method, we multiply both sides of the equation by the product of the denominators of all the fractions. This will clear the fractions and result in an equivalent equation that can be solved by using algebraic techniques. For example, to solve the equation 3/x = 9/20, we multiply both sides by 20x, which is the product of the denominators. This gives us:

3/x = 9/20 20x(3/x) = 20x(9/20) 60 = 9x x = 60/9 x = 20/3

We can check our solution by plugging it back into the original equation and verifying that both sides are equal.

## Least Common Denominator Method

The least common denominator method is another technique that can be used to solve fractional equations by eliminating the fractions. The least common denominator method is based on the idea that if two fractions have the same denominator, then they can be added or subtracted by adding or subtracting their numerators. For example, if a/b + c/b = d/b, then a + c = d.

To use the least common denominator method, we find the least common denominator (LCD) of all the fractions in the equation. The LCD is the smallest positive number that is divisible by all the denominators. Then, we multiply both sides of the equation by the LCD, which will clear the fractions and result in an equivalent equation that can be solved by using algebraic techniques. For example, to solve the equation x-2/x+2 = 3/5, we find that the LCD of x+2 and 5 is 5(x+2). We multiply both sides by 5(x+2), which gives us:

x-2/x+2 = 3/5 5(x+2)(x-2/x+2) = 5(x+2)(3/5) 5(x-2) = 3(x+2) 5x - 10 = 3x + 6 2x = 16 x = 8

We can check our solution by plugging it back into the original equation and verifying that both sides are equal.

## Conclusion

In this article, we have reviewed some methods and examples of solving fractional equations that are aligned with the Common Core Algebra 2 standards. Fractional equations are equations that contain fractions with variables in the numerator or denominator. Solving fractional equations involves finding the value of the variable that makes the equation true. We can use techniques such as the cross-product method or the least common denominator method to eliminate the fractions and obtain an equivalent equation that can be solved by using algebraic techniques. Solving fractional equations is an important skill that can help us model and solve real-world problems involving ratios, proportions, rates, and more.

If you need more help with solving fractional equations or other topics in Algebra 2, you can check out some online resources such as [Algebra 2 Common Core - Solutions and Answers] or [Algebra 2: A Common Core Curriculum - Solutions and Answers]. You can also find more examples and explanations on [Mathematics LibreTexts].

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