Советы от нейросети в категории simplification

Simplifying Rational Expressions

2024-03-05 18:06:47

First, we need to simplify the given equation by combining like terms and dividing both the numerator and denominator by the greatest common factor (x). This will give us the equation (1/(x+3))-(1/3(x^2-3x+9)). Next, we need to factor the denominator of the second fraction to get (1/(x+3))-(1/3(x-3)(x-3)). Now we can combine the two fractions by finding a common denominator, which in this case is 3(x^2-3x+9). This will give us the equation (3(x-3)-x+3)/(3(x^2-3x+9)). Simplifying this further, we get (2x-6)/(3x^2-9x+27). It might also be useful to note that we can further factor the denominator to get (2x-6)/(3(x-3)(x-3)). Now, to get the final solution, we can cancel out the common factor of (x-3) in the numerator and denominator, which will leave us with the final answer of 2/(3(x-3)). This is the simplified form of the given equation.

Simplify Fraction

2023-12-24 17:03:29

To simplify a fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. In this case, the GCF of 5 and 28 is 1, so we can divide both numbers by 1 to get the simplified form.

Therefore, the simplified fraction is 5*227/1*28 = 5*227/28 = 1135/28.

To shortcut the dividing process, we can use prime factorization method which breaks down the numbers into factors.

For the numerator 1135, the prime factorization is 5*227, while for the denominator 28, the prime factorization is 2*2*7. Then, we can cancel out common factors and simplify.

So, the simplified fraction is still 5*227/28 = 1135/28.

Simplifying and solving equations with exponents

2023-12-17 20:39:44

Firstly, it's important to remember that when solving equations with exponents like this, you'll want to simplify the bracketed expressions first before raising them to a power. So in this case, you would simplify the expressions inside the brackets to get (6)^2 and (6x)^2.
Next, you can apply the power of a power rule, which states that when raising a power to another power, you simply multiply the exponents together. So in this case, (6)^2 becomes 6^(2*2) and (6x)^2 becomes (6x)^(2*2).
After simplifying the expressions, you should end up with (36)^2 and (36x)^2.
Finally, you can combine the terms by multiplying the coefficients together and keeping the bases the same. So for the first term, you would have (36)^2 = 36*36 = 1296 and for the second term, you would have (36x)^2 = 36^2 * x^2 = 1296x^2.
Don't forget the order of operations- multiplication and division are done first, followed by addition and subtraction. So make sure to distribute any coefficients before multiplying, as shown in step 4.
If you're ever struggling with exponent rules, just remember the mnemonic PEMDAS- Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. This can help you keep track of which operations to do first.
Another helpful tip is to break down the problem one step at a time and write out each step clearly. This will help you avoid making mistakes or getting lost in the calculations.
Lastly, always double check your answer by plugging the value of x back into the original equation to make sure it holds true. This can save you from getting the wrong answer due to a small mistake.