Question

Выполнить действия с алгебраическими дробями

Answer 1

а+b+2a+4b = 3a+6b=3(a+2b)=a+2b
       15               15       15            5
b+c-b+2c=3c=c
        3a     3a   a

Answer 2

Working with Algebraic Fractions

To work with algebraic fractions, we need to perform various operations such as simplification, addition, subtraction, multiplication, and division. Let's go through each of these operations step by step.

Simplification of Algebraic Fractions

Simplification involves reducing the fraction to its simplest form by canceling out common factors in the numerator and the denominator.

For example: 1. Simplify the algebraic fraction \( \frac{4x}{12} \). - The simplified form of \( \frac{4x}{12} \) is \( \frac{1}{3}x \).

Addition and Subtraction of Algebraic Fractions

When adding or subtracting algebraic fractions, we need to find a common denominator and then perform the operation.

For example: 1. Add or subtract \( \frac{7}{x} \) and \( \frac{7}{5} \). - To add or subtract \( \frac{7}{x} \) and \( \frac{7}{5} \), we need to find a common denominator, which is \( 5x \). The result will be \( \frac{7x+7}{5x} \).

Multiplication and Division of Algebraic Fractions

Multiplication of algebraic fractions involves multiplying the numerators together and the denomin