Given:
[tex]\frac{x+1}{3y}+\frac{x-2}{4y}-\frac{x+3}{6y}[/tex]
To solve it, follow the steps below.
Step 01: Find a common denominator.
Factoring the coefficients:
3, 4, 6 | 2
3, 2, 3 | 2
3, 1, 3 | 3
1, 1 ,1
2*2*3 = 12
The common denominator can be 12y.
Step 02: Write the function using the common denominator.
[tex]\begin{gathered} \frac{x+1}{3y}+\frac{x-2}{4y}-\frac{x+3}{6y} \\ \frac{4*(x+1)+3(x-2)-2(x+3)}{12y} \end{gathered}[/tex]
Step 03: Solve the function.
[tex]\begin{gathered} \frac{4*x+4*1+3*x+3*(-2)-2*x-2*3}{12y} \\ \frac{4x+4+3x-6-2x-6}{12y} \end{gathered}[/tex]
Adding the like-terms.
[tex]\begin{gathered} \frac{4x+3x-2x+4-6-6}{12y} \\ \frac{5x-8}{12y} \end{gathered}[/tex]
Answer:
[tex]\frac{5x-8}{12y}[/tex]
