Find the simplest common denominator to process! Thank you

The answer is: -6x(x+1)(x-2).

Let's change the second equation to -3 (x-2)).

1. The least common multiple of the coefficient: -6x

2. The highest power of the same letter or factor: (x+1)(x+2) 3, -6x(x+1)(x-2).

2（x-2）^2=2（x-2）（x-2）

The simplest common denominator is 6x(2-x)(x+1)(x+2)(x-2)6 because 2 times 3

Other sample questions. x-2 and 3x+6 and x's cube-4x's simplest common denominator.

3x+6=3(x+2)

x^3-4x=x(x+2)(x-2)

So the simplest common denominator is 3x(x+2)(x-2).

The simplest common denominator of x(x-1) and x-square-1 and x-square-2x+1.

x²-1=(x+1)(x-1)

x²-2x+1)=(x-1)(x-1)

So the simplest common denominator is x(x-1)(x+1)(x-1).

Factor the denominator of each fraction.

Take the least common multiple of the coefficient of each denominator, where the factor of the letter or the factor containing the letter is the base of the power should be taken, the factor of the power of the same letter or the factor containing the letter takes the largest exponent, multiply the above obtained formulas, and the simplest common denominator is obtained, and the numerator and denominator of the original fraction are multiplied by an appropriate integer, so that the denominator of each fraction is turned into the simplest common denominator.

In fact, this is the same as when adding and subtracting different denominator fractions in elementary school, you must first find the least common multiple of the denominator. For fractions, to find the least common multiple of the denominator, the same reason, we must first understand what are the factors of the denominator, which requires understanding what are the factors of the denominator in each factor, and find the simplest common denominator of the denominator, similar to finding the least common multiple of the denominator when adding and subtracting fractions.

The minimum common denominator of the two fractions is required, which can be done by following these steps:

Find the lowest round-bend common multiple (lcm) of the denominator of the two fractions.

Multiply the numerators of the two fractions by the denominator of each other to maintain the equivalence relationship.

Set the denominator of the resulting new score to the least common multiple.

The ratio of the numerator of the new fraction to the common denominator of the simplest cavity chain is judged to obtain the fraction in the simplest form.

How does y-x in item b become x-y.

It's because y-x=-（x-y）

Find the simplest common denominator"Usually rock imitation is a problem that arises when dealing with two or more fractions. In this case, we need to find a number that is divisible by the denominator of all fractions, which is called"Least common multiple"（lcm）。

Here are the steps to find the least common multiple of two numbers:

1.Find all the prime factors of two numbers. A prime factor is a prime number that is divisible by a given number. For example, the prime factor of the number 8 is 2 because 8 is divisible by 2 and 2 is a prime number in its own right.

2.Out of all prime factors, select the maximum power of each prime factor. For example, if you have two numbers, 12 and 18, the prime factors of 12 are 2 and 3, where the power of 2 is 2 (because 12 = 2*3) and the power of 3 is 1 (because there is only one 3).

For 18, a power of 2 is 1 and a power of 3 is 2. So, the maximum power of 2 we choose is 2, and the maximum power of 3 is 2.

3.Multiply all the selected maximum jujube codes to the nearest common multiple. In our example, we have 2 = 4 and 3 = 9, so the least common multiple is 4 * 9 = 36.

This method can be extended to three or more numbers. When you're dealing with fractions, just find the least common multiple of all the denominators, and then multiply the numerator and denominator of each fraction by the necessary number so that all the denominators become the least common multiple, so you can get the simplest common denominator.

To request the simplest common denominator, you can follow these steps:

Find the denominator of all fractions.

Find the least common multiple (LCM) of these denominators.

Multiply the reflex rise numerator of all fractions by an appropriate multiple so that their denominator is equal to the least common multiple.

In this way, all scores have the same denominator.

As an example, let's say we have the following two scores: 1 3 and 2 5.

Find the denominator: The denominator of the fraction 1 3 is 3, and the denominator of the fraction 2 5 is 5.

Find the least common multiple: The least common multiple of 3 and 5 is 15.

Adjust the molecule: Multiply the numerator of 1 3 by 5 to get 5 15;Multiply the numerator of 2 5 by 3 to get 6 15.

Now, both fractions have a denominator of 15, and their simplest common omission old denominator is 15.

So, the simplest common denominator is 15. You can follow this method to convert the denominator of other fractions to the simplest common denominator. Note that this is only a method for the case of two fractions.

If there are multiple fractions, they can be compared and adjusted one by one until they have the same denominator.

Decomposition factor method: decompose the denominator of each fraction into prime factors, find out their common factors and the smallest non-starting and canceling same factor, and multiply these different factors by the side splits to obtain the simplest common denominator.

General Fractionation: The denominator of each fraction is reduced to the same denominator, and then the numerators are merged to reduce the resulting fraction to the simplest form.

When finding the simplest common denominator, decompose the denominator into factors, turn all expressions into the form of products, and take the product of the highest power of all denominator factors to determine the simplest common denominator.

For example, find the simplest common denominator of x-2 and 3x+6 and x's cube-4x as follows:

3x+6=3(x+2)

x^3-4x=x(x+2)(x-2)

Therefore, the minimum common denominator is 3x(x+2)(x-2).

The product of the least common multiple of each denominator coefficient and the highest power of the letter factor is usually taken as the common denominator, and such a common denominator is called the simplest common denominator.

General method: If the denominator is a monomial, then the simplest common denominator is the least common multiple of each coefficient, the highest power of the same letter, and all the different letters are written in the product.

If each denominator is a polynomial, you can factor each denominator into the least common multiple of the numerical coefficient of each denominator, and take the highest power of the factor where the letter (or integer with letters) is the power of the base number.

Definition: Generally, the product of the highest power of all factors of each denominator is taken as the common denominator, which is called the simplest common denominator.

Method: 1. The denominator is mononomial: take the product of the least common multiple of the integer coefficient and the highest power of the same letter, and only the letter in a monomial is taken as part of the simplest common denominator together with its exponent.

2. The denominator is a polynomial: first decompose the factor, and then take the product of the least common multiple of the integer coefficient and the highest power of the same letter.

It is the least common multiple of the denominator, and if the common multiple cannot be found, just use short division......Short division should do.

There is no other way.

The method of determining the simplest common denominator: 1. Factorize the denominator of each fraction;

2. Take the least common multiple of each denominator coefficient;

3. All the factors that appear in the letters or the power of the factors containing the letters should be taken;

4. The factor of the power of the same letter or the factor containing the letter takes the exponent as the largest;

5. Multiply all the above formulas to get the simplest common denominator;

6.The numerator and denominator of each fraction are multiplied by an appropriate integer, so that the denominator of each fraction is reduced to the simplest common denominator.

Method for determining the simplest common denominator:

1. Take the least common multiple of each denominator coefficient.

2: All the letters that appear separately together with their exponents are used as a factor of the simplest common denominator 3: The exponents of the same letter are taken as the highest number of times The product of the resulting factors is the simplest common denominator.

x^2+x-6=(x+3)(x-2)

x^2-9=(x-3)(x+3)

x^2+5x+6=(x+3)(x+2)

So the simplest common denominator is (x+3)(x-2)(x-3)(x+2)x-2 and 3x+6 and the cube of x-4x, the simplest common denominator 3x+6=3(x+2).

x^3-4x=x(x+2)(x-2)

So the simplest common denominator is 3x(x+2)(x-2).

x(x-1) and x-squared-1 and x-squared-2x+1 The simplest common denominator x -1=(x+1)(x-1).

x²-2x+1)=(x-1)(x-1)

So the simplest common denominator is x(x-1)(x+1)(x-1).