Советы от нейросети в категории fractions

Solving a Complex Equation

2024-12-27 21:17:12

Solution:
First, we need to combine the fractions on the left side of the equation by finding their lowest common denominator, which is (2x-1)(2x^2+x-1). This gives us:
(2x^2+x-1) + 4(2x^2+x-1) = 4(2x-1)(2x^2+x-1)
Next, we can distribute the 4 on the right side and simplify the equations:
2x^2 + x - 1 + 8x^2 + 4x - 4 = 8x^3 - 4x^2 + 4x - 4
Then, we can combine like terms on both sides:
10x^2 + 5x - 5 = 8x^3 - 4x^2 + 4x - 4
Now, we can move all the terms to one side, leaving 0 on the other:
8x^3 - 14x^2 + x - 1 = 0
This equation can be solved using the Rational Root Theorem, which states that any rational root of a polynomial is in the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. Using this knowledge, we can find that the rational roots of this equation are -1/2 and 1/4.
We can then use synthetic division to find that -1/2 is a root, leaving us with a new equation:
(2x - 1)(8x^2 - 19x + 2) = 0
From this, we know that 2x - 1 = 0 or 8x^2 - 19x + 2 = 0. Solving these equations gives us the solutions x = 1/2 and x = 1/8. Therefore, the solution to the given equation is x = 1/2 or x = 1/8.

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)

Adding Fractions Like a Pro

2024-03-03 00:06:18

Buckle up, this is going to be a wild ride. In order to add these fractions, we first have to make sure that the denominators are the same. We can do this by finding the least common denominator (LCD). In this case, the LCD is 30. We then multiply each fraction by the equivalent of 1, which is 30/30. This will give us the new numerators 64/30 and 39/30. Now we can add the numerators, obtaining a final answer of 103/30. However, this is not in simplest form and we must reduce it. The greatest common divisor (GCD) of 103 and 30 is 1, so we can simply write the final answer as 103/30. Now go treat yourself to some ice cream, you deserve it.

Solving Fraction Addition

2024-03-03 00:06:09

To solve this problem, you first need to convert all the mixed numbers to improper fractions. We can rewrite 2 1/8 as 17/8 and 9/10 as 18/20.

Now, we can add the fractions by finding a common denominator. In this case, the lowest common denominator is 40. So, 17/8 becomes 85/40 and 18/20 becomes 36/40.

Next, we can combine the fractions by adding the numerators. We get 121/40 as the new fraction.

Similarly, we can find a common denominator for the second equation, which is 30. So, 2/15 becomes 8/30 and 1/10 becomes 3/30.

Now, we can combine the fractions and get 11/30 as the new fraction.

Finally, we can divide 121/40 by 11/30 which gives us the final answer of 33 3/4.

Solving a Division Problem

2024-02-20 15:04:06

51/81 = 0.62963

Prompt title

2024-02-07 20:49:45

Чтобы сократить дробь 324 и 378, нужно найти их наименьшее общее кратное и поделить каждое число на него. НОК (324, 378) = 756. Теперь получаем дроби 324/756 и 378/756. Но если хотите сразу сократить дроби, то они все равны 3/7. Таким образом, ответ равен 3/7.

Solving Fractions

2024-02-06 12:13:51

Solution:

First, we need to convert the mixed number 52/8 into an improper fraction, which is equivalent to 6 4/8. Then, we can add the fractions of 2/5 and 24/17 by finding a common denominator, which in this case is 85. So, we have (2*17/5*17) + (24*5/17*5) = 34/85 + 120/85 = 154/85. Now, we can divide 154/85 by 6 4/8 by multiplying the reciprocal 8/54. The final answer is 7/12.

Explanation:

The key to solving this problem is to understand the concept of converting mixed numbers to improper fractions and finding common denominators. By converting both mixed numbers into improper fractions, we can easily add them together to get an equivalent fraction with a common denominator. After that, we can simply divide the resulting fraction by multiplying its reciprocal. Remember to always simplify the final answer, which in this case is 7/12.

Remember to double check your work and always show your steps.

Solving a Fraction Subtraction Problem

2023-11-12 10:23:31

To solve this problem, we need to find the common denominator of 87 and 116, which is 1,004. Then, we can rewrite the fractions as 116/1,004 and 87/1,004. Next, we can subtract the numerators, giving us a result of 29/1,004. This cannot be simplified any further, so the final answer is 29/1,004. Remember to always check for accuracy by plugging in the values to the original equation!

Solving Fractions

2023-11-12 10:23:27

To solve the problem 1/87-1/116, we need to first find the common denominator. In this case, the common denominator is 10,292. Therefore, we can rewrite the problem as (116*89)/(10,292) - (87*94)/(10,292). Simplifying this, we get (11,9644)/(10,292) - (8,1780)/(10,292). Combining like terms, the final answer is 3,7864/10,292, which can be simplified to 0.3688.

Note: If you encounter a similar problem in the future, keep in mind that the key is to find the common denominator and then simplify the expression. Keep practicing and soon you'll be able to do these calculations with your eyes closed!