26x+14 / 24x^2 + 27x + 3.
Explanation:
5/4x+1- 1/3(2x+1)
(5/(4x+1))-(1/(6x+3))
(5/(4x+1))-(1/(6x+3)) = (5(6x+3) - 1(4x+1))/(4x+1)(6x+3) = 30x+15 - 4x-1 / 24x^2 + 27x + 3 = 26x+14 / 24x^2 + 27x + 3.
Here are the steps on how to solve it:
1. Simplify the expressions in the numerator and denominator.
2. Find a common denominator for the two fractions.
3. Subtract the numerators and simplify the expression.
The answer is 26x+14 / 24x^2 + 27x + 3.
bardai
To simplify the expression (5/(4x+1)) - (1/(6x+3)), we need to find a common denominator for the two fractions and then combine them.
Step 1: Find the common denominator
The common denominator for the fractions (4x+1) and (6x+3) is the product of their denominators, which is (4x+1)(6x+3).
Step 2: Convert both fractions to have the common denominator
To convert the first fraction, multiply both the numerator and denominator by (6x+3):
(5/(4x+1)) * ((6x+3)/(6x+3)) = (5*(6x+3))/((4x+1)*(6x+3)).
To convert the second fraction, multiply both the numerator and denominator by (4x+1):
(1/(6x+3)) * ((4x+1)/(4x+1)) = (1*(4x+1))/((6x+3)*(4x+1)).
Step 3: Combine the fractions
Now, the expression becomes:
(5*(6x+3))/((4x+1)*(6x+3)) - (1*(4x+1))/((6x+3)*(4x+1)).
Step 4: Simplify the expression
Since the denominators are the same, we can combine the numerators:
(5*(6x+3) - (4x+1))/((4x+1)*(6x+3)).
Now, distribute the multiplication:
(30x + 15 - 4x - 1)/((4x+1)*(6x+3)).
Combine like terms in the numerator:
(26x + 14)/((4x+1)*(6x+3)).
The simplified expression is:
(26x + 14)/((4x+1)*(6x+3)).
chatgpt