Add or subtract
2/x^2+1/x
2/x+3/2x-3/5x
7/x^2+5/x
help me step by step
Create common denominators for all terms and add the numerators.
In the first case,
2/x^2 + 1/x = 2/x^2 + x/x^2 = (2+x)/x^2
To add or subtract rational expressions, you need to have a common denominator. Let's go through each of the exercises step by step:
Exercise 1:
2/x^2 + 1/x
Step 1: Identify the common denominator.
In this case, the common denominator is x^2 because both expressions have it as a denominator.
Step 2: Adjust the numerators.
To do this, we multiply the first term's numerator (2) by x to get a common denominator of x^2, and the second term's numerator (1) by x^2, which already has a common denominator.
So, the expression becomes: (2x/x^2) + (1/x)
Step 3: Combine the numerators over the common denominator.
(2x + 1) / x^2
Exercise 2:
2/x + 3/2x - 3/5x
Step 1: Identify the common denominator.
To find the common denominator, we need to find the least common multiple (LCM) of the denominators, which are x, 2x, and 5x.
The LCM of x, 2x, and 5x is 10x.
Step 2: Adjust the numerators.
Multiply each term's numerator by the factors needed to obtain the common denominator.
The expression becomes: (2 * (10x/10x)) + (3 * (5/5x)) - (3 * (2/2x))
Simplified version: (20x/10x) + (15/5x) - (6/2x)
Step 3: Combine the numerators over the common denominator.
Simplify the numerators by dividing:
(2) + (3/x) - (3/x)
Final simplified expression: 2 + (3/x) - (3/x)
Exercise 3:
7/x^2 + 5/x
Step 1: Identify the common denominator.
In this case, the common denominator is x^2 because the first term has it as a denominator.
Step 2: Adjust the numerators.
To do this, we multiply the first term's numerator (7) by x to get a common denominator of x^2.
So, the expression becomes: (7x/x^2) + (5/x)
Step 3: Combine the numerators over the common denominator.
(7x + 5) / x^2
Final simplified expression: (7x + 5) / x^2
Remember to always check if there are any further simplifications possible after adding or subtracting the rational expressions.