Question

What has to be added to the sum of 3/4 and 4/3 to get 3?

Answer 1

Given

What has to be added to the sum of 3/4 and 4/3 to get 3?

Solution

Let's assume the number to be x

`(3)/(4)+(4)/(3)+x=3`

Then, we solve for x

We can multiply all through by the L C M 12 to clear the fraction

`12*(4)/(3)+12*(3)/(4)+x*12=3*12`

simplify

`\begin{gathered} 16+9+12x=36 \\ \end{gathered}`

collect the like terms

`\begin{gathered} 25+12x=36 \\ 12x=36-25 \\ 12x=11 \\ \end{gathered}`

Divide both sides by 12

`\begin{gathered} (12x)/(12)=(11)/(12) \\ \\ x=(11)/(12) \end{gathered}`

The final answer