Explanation:
To solve the equation (1/(y + 5)) - (2/(y - 4)) = -9/(y^2 + y - 20), we can follow these steps:
Step 1: Factor the denominator of the third term.
The denominator y^2 + y - 20 can be factored as (y + 5)(y - 4).
Step 2: Find a common denominator for all terms.
The common denominator for the three terms is (y + 5)(y - 4).
Step 3: Simplify each term by multiplying the numerators by the appropriate factors.
(1 * (y - 4))/(y + 5)(y - 4) - (2 * (y + 5))/(y + 5)(y - 4) = -9/(y + 5)(y - 4)
Simplifying further:
(y - 4)/(y + 5)(y - 4) - (2y + 10)/(y + 5)(y - 4) = -9/(y + 5)(y - 4)
Step 4: Combine like terms.
(y - 4 - (2y + 10))/(y + 5)(y - 4) = -9/(y + 5)(y - 4)
Simplifying further:
(y - 4 - 2y - 10)/(y + 5)(y - 4) = -9/(y + 5)(y - 4)
(-y - 14)/(y + 5)(y - 4) = -9/(y + 5)(y - 4)
Step 5: Cancel out the common factors.
- y - 14 = -9
Step 6: Solve for y.
- y = -9 + 14
- y = 5
y = -5
So the solution to the equation is y = -5.