Which Of The Following Is Equal To
"Which of the following is equal to" is a type of math question that asks you to compare two or more expressions and determine which one is equal to a given value. These questions can be challenging, but they are also a great way to test your understanding of mathematical concepts.
To solve these types of questions, you need to carefully analyze the expressions and identify any similarities or differences. You can also use algebraic manipulation to simplify the expressions and make them easier to compare.
Here are some tips for solving "which of the following is equal to" questions:
- Read the question carefully and identify the given value.
- Analyze the expressions and identify any similarities or differences.
- Use algebraic manipulation to simplify the expressions.
- Compare the expressions and identify the one that is equal to the given value.
Here are some examples of "which of the following is equal to" questions:
Question 1:
Which of the following is equal to 2^3 * 5^2? Answer:
(2 * 5)^2 = 10^2 = 100 Question 2:
Which of the following is equal to (1 + 2 + 3)^2 - 4^2? Answer:
(6)^2 - 4^2 = 36 - 16 = 20 Question 3:
Which of the following is equal to (x^2 + 1) / (x^2 - 1)? Answer:
(x^2 + 1) / (x^2 - 1) = (x + 1)(x - 1) / (x^2 - 1) = x + 1 Question 4:
Which of the following is equal to (2x - 1)/(x + 1) - (x - 2)/(x - 1)? Answer:
(2x - 1)/(x + 1) - (x - 2)/(x - 1) = (2x^2 - 2x - x + 2)/(x^2 + x - 1) = x^2 - x + 2 / (x^2 + x - 1) To solve this question, we can first factor the expressions in the numerator and denominator. The numerator can be factored as (x – 1)(2x + 2), and the denominator can be factored as (x – 1)(x + 1). This gives us:
(2x - 1)/(x + 1) - (x - 2)/(x - 1) = (x - 1)(2x + 2) / (x - 1)(x + 1) - (x - 1)/(x - 1)(x + 1) We can then cancel the common factors in the numerator and denominator to get:
(2x + 2) / (x + 1) - 1 / (x + 1) = 2x + 2 - 1 / (x + 1) = 2x + 1 / (x + 1) Finally, we can simplify the expression by multiplying the numerator and denominator by (x – 1) to get:
(2x + 1) / (x + 1) = (2x + 1)(x - 1) / (x + 1)(x - 1) = 2x^2 + x - 1 Therefore, the answer to the question is 2x^2 + x – 1.
These are just a few examples of "which of the following is equal to" questions. With practice, you will be able to solve these types of questions quickly and accurately.
