# How do you solve #(y+4)/(y-2)+6/(y-2)=1/(y+3)#?

Solution:

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To solve the equation (y+4)/(y-2)+6/(y-2)=1/(y+3), we can start by finding a common denominator for the fractions on the left side of the equation, which is (y-2)(y+3). Multiplying each term by this common denominator, we get (y+4)(y+3) + 6(y+3) = (y-2).

Expanding and simplifying the equation, we have y^2 + 7y + 12 + 6y + 18 = y - 2.

Combining like terms, we get y^2 + 13y + 30 = y - 2.

Rearranging the equation, we have y^2 + 12y + 32 = 0.

Factoring the quadratic equation, we have (y + 4)(y + 8) = 0.

Setting each factor equal to zero, we have y + 4 = 0 or y + 8 = 0.

Solving for y, we find y = -4 or y = -8.

Therefore, the solutions to the equation are y = -4 and y = -8.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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