158k views
1 vote
1/y+5 - 2/y-4 = -9/y²+y-20

User Owenizedd
by
8.1k points

1 Answer

2 votes

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
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories