5/(2y+6)+1/(y-2)=3/(y+3)?
To solve the equation 5/(2y + 6) + 1/(y - 2) = 3/(y + 3), we can follow these steps:
Step 1: Find a common denominator.
To add or subtract fractions, we need to have a common denominator. In this case, the common denominator will be (2y + 6) * (y - 2) * (y + 3).
Step 2: Rewrite each fraction with the common denominator.
Rewriting the equation with the common denominator, we get:
(5*(y - 2)*(y + 3))/(2y + 6)(y - 2)(y + 3) + (1*(2y + 6)*(y + 3))/(y - 2)(2y + 6)(y + 3) = (3*(2y + 6)*(y - 2))/(y + 3)(2y + 6)(y - 2)
Step 3: Simplify the equation.
After simplifying the equation by canceling out common factors, we get:
5(y - 2) + (2y + 6) = 3(2y + 6)
Step 4: Solve for y.
Expand and simplify the equation:
5y - 10 + 2y + 6 = 6y + 18
Combine like terms:
7y - 4 = 6y + 18
Subtract 6y from both sides to isolate the y term:
y - 4 = 18
Add 4 to both sides:
y = 22
So the solution to the equation 5/(2y + 6) + 1/(y - 2) = 3/(y + 3) is y = 22.