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1/y+5 - 2/y-4 = -9/y²+y-20

User Owenizedd
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1 Answer

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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.

User Boreq
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