Советы от нейросети в категории algebra

Simplifying Complex Fraction

2024-03-05 18:09:34

Simplify the expression first before solving. Remember that when dividing fractions, you can multiply the first fraction by the reciprocal of the second. Hence,

(x^5/x(x+3))-(x-3/3(x^2-3x+9))

becomes

(x^5/x(x+3))-((x-3)(x+3)/3(x-3)(x+3))

which simplifies to

x^4-(x+3)/3(x^2-9)

Now, the expression can be written as

(x^4-x-3)/3x^2-27)

or

(x^2-3)(x^2+1)/3(x^2-3)(x+3)=

(x^2+1)/3(x+3)

Expressions with factors of x-3 can be cancelled out, leaving us with the final answer of

1/3(x+3)

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.

Solving Equations with One Variable

2024-02-06 21:13:45

Dear User,

You have provided three equations consisting of one variable, x. In each equation, the value of x is different. This can be a bit confusing, but don't worry, I am here to help you understand them.

Prompt Title

The different values of x in each equation suggest that they are unrelated to each other. Hence, there is no solution or relationship that can be established between them.

This can be better understood by solving each equation separately. So, let's begin!

[х]= -2
This equation has only one solution which is -2. This means that whatever value x holds, if [х] is equal to -2, then that value of x must be -2.
[х]=6
Similarly, this equation also has only one solution which is 6. This means that the value of x must be 6, if [х] is equal to 6.
[-х]=6,7
This equation has two solutions which are -6 and -7. This means that if [-х] is equal to 6, then the value of x can be either -6 or -7.

I hope this explanation has cleared your confusion. Just remember, each equation has a unique solution which can be found by plugging in the value of x within the brackets.

Relevant Category

Mathematics, Algebra, Equations

Solve the equation

2024-02-06 12:17:05

2 + 15 = 17

Finding the minimum value for the length of the longest segment

2024-02-05 23:31:44

The minimum value for the length of the longest segment is 8. This can be proven by constructing a 5-sided polygon with the given segments, which satisfies the requirement of being a pentagon. In addition, by assuming a smaller value for the longest segment, it can be proven that it is not possible to construct a 5-sided polygon. In order to construct the pentagon, the angles of the polygon must satisfy the triangle inequality, which states that the sum of the lengths of any two sides must be greater than the length of the third side. By drawing diagrams and doing some algebraic manipulations, it can be shown that the smallest possible value for the longest segment is 8. This is because the sum of the two shortest segments must be greater than the sum of the two longer segments in order to satisfy the triangle inequality. Therefore, all five segments must have lengths 1, 2, 3, 4, and 5 respectively, and by rearranging these segments, a 5-sided polygon can be constructed. This is the minimum value for the length of the longest segment, and any value smaller than 8 will not fulfill the requirements of the problem.

Simplifying an Expression

2024-01-31 15:38:30

Your task is to simplify the given expression: 2000000000000000000000000000000000000000000000000-2. Simplifying this expression involves combining like terms or reducing it to the closest possible form. In this case, the first step is to rearrange the expression so that the smaller number is being subtracted from the larger number. This will make the calculation easier to visualize. So our expression now becomes 2000000000000000000000000000000000000000000000000-0-2. From here, we can simplify by subtracting 0 from the larger number, which would result in the same number. So our expression becomes 2000000000000000000000000000000000000000000000000-2. Next, we can combine the two numbers by subtracting them, which results in the simplified expression 2000000000000000000000000000000000000000000000000. This is the final answer: 2000000000000000000000000000000000000000000000000. The key to simplifying expressions is to identify and eliminate unnecessary terms. In this case, the number 0 has no effect on the final answer and can be removed. I hope this solves your problem!

Solving Quadratic Equations

2024-01-30 11:22:41

а) Чтобы решить уравнения вида ax2 + bx + c = 0, можно воспользоваться формулой дискриминанта: x1,2 = (- b ± √(b2 - 4ac)) / 2a, где a, b и c - коэффициенты уравнения. Таким образом, для уравнения х2 + 10х + 9 = 0 получаем следующее решение: x1,2 = (- 10 ± √(102 - 4 * 1 * 9)) / 2 * 1 = (- 10 ± 8) / 2 = - 9 или - 1. Ответ: x1 = - 9, x2 = - 1.

б) Повторим тот же алгоритм для уравнения 3х2 – 9 = 0: x1,2 = (- 0 ± √(02 - 4 * 3 * (- 9))) / 2 * 3 = (- 0 ± 6) / 6 = - 1 или 3. Ответ: x1 = -1, x2 = 3.

в) Для уравнения 5х2 – х + 2 = 0 необходимо сначала привести уравнение к виду ax2 + bx + c = 0, вынеся общий коэффициент a за скобки: 5(х2 – 0.2х) + 2 = 0. Теперь решаем аналогично: x1,2 = (- (-0.2) ± √((-0.2)2 - 4 * 5 * 2)) / 2 * 5 = (0.2 ± √(0.04 - 40)) / 10 = (0.2 ± √(- 39.96)) / 10. Следовательно, действительных корней у этого уравнения нет.

Это были все решения уравнений в данном примере. Учтите, что использование формулы дискриминанта возможно только для квадратных уравнений. В других случаях может потребоваться применение других методов решения.

Solving an Equation

2024-01-25 09:59:48

To solve this equation, we need to start by combining like terms. First, let's combine the two 'x' terms by adding them together. This gives us 4x. The equation now becomes 4x-5=10. Next, we need to move the constant term, -5, to the other side of the equation by adding 5 to both sides. This gives us 4x=15. Finally, we can solve for x by dividing both sides by 4. This gives us x=3. So the solution to the equation is x=3.

Find the value of x

2023-12-19 22:38:36

При правильной реализации данной задачи, необходимо обратиться к математической теории о корнях степенных уравнений. В данном случае, необходимо найти значение переменной x, который удовлетворяет уравнению 4√x-2=0. В качестве начального шага, выразите x в виде х+2/4=0, затем приведите уравнение к степени, чтобы избежать неоднозначности. Далее, свяжите нуль и корни степени в урaвнении, чтобы умножить оба члена на 4√х. Дополнительным шагом являются вычисления, которые заключаются в заданной формуле. И наконец, в ответе будет получено значение переменной x=1/2. Это значение удовлетворяет исходному уравнению и доказывает его правильность.

Advice on Solving the Problem of Two Typists

2023-12-13 15:48:57

Для решения данной задачи необходимо написать систему уравнений. Пусть x и y - время работы первой и второй наборщиц соответственно. Тогда, учитывая, что общее время работы составляет 6 часов, исходя из условия задачи можно составить следующее уравнение:

x + y = 6

Также, известно, что если первая наборщица напечатает половину рукописи, то она затратит на это x / 2 часов, а если вторая напечатает оставшуюся половину, то ее работа будет затрачена на (6 - x / 2) часов. Кроме того, из условия задачи следует, что общее время работы составляет 12.5 часов, поэтому можно составить следующее уравнение:

x / 2 + (6 - x / 2) = 12.5

Решая данную систему уравнений, получим, что x = 10 и y = 4. Таким образом, первая наборщица может выполнить всю работу за 10 часов, а вторая - за 4 часа. Чтобы убедиться в правильности данного решения, можно подставить полученные значения в исходные уравнения и увидеть, что они выполняются.