Question

How do you simplify $\dfrac{y}{2y}+\dfrac{y+2}{y}$ ?

Answer 1

Hint: In this question, we have to simplify the given algebraic equation. Thus, we will apply the basic mathematical rules to get the solution. First, we will cancel out the same variables in the division. After that, we will apply the least common multiple method in the denominator and get a new fraction. Then we will apply the algebraic identity $a(b+c)=ab+ac$ in the numerator and make the necessary calculations to get the required result for the solution.

Complete step by step solution:
According to the question, we have to simplify the algebraic equation.
Thus, we will use the basic mathematical rule to get the solution.
The algebraic equation given to us is $\dfrac{y}{2y}+\dfrac{y+2}{y}$ ------------- (1)
First, we will cancel out the same variables in the division n equation (1), we get
$\Rightarrow \dfrac{1}{2}+\dfrac{y+2}{y}$
Now, we will take the least common multiple of the denominator in the above equation, that is we get the new denominator equal to the multiplication of the given denominator. For the new numerator, we will multiply the first term numerator with the second term denominator and add it in the multiplication of the second term numerator with the first term denominator, we get
$\Rightarrow \dfrac{y+2(y+2)}{2y}$
Now, we will apply the distributive property $a(b+c)=ab+ac$ in the numerator of the above equation, we get
$\Rightarrow \dfrac{y+2y+2(2)}{2y}$
On further simplification of the above equation, we get
$\Rightarrow \dfrac{3y+4}{2y}$
Now, we will split the above fraction with respect to the addition sign, we get
$\Rightarrow \dfrac{3y}{2y}+\dfrac{4}{2y}$
Now, we again cancel out the same variable and the terms in the division, we get
$\Rightarrow \dfrac{3}{2}+\dfrac{2}{y}$ which is our required answer.

Note: While solving the problem, keep in mind the formulas you are using and mention in the steps wherever is required to avoid mathematical errors. One of the alternative methods to solve this problem is first to take the LCM of the denominator and then do the necessary calculations to get the required solution.