# How do you solve #(y^2+5y-6)/(y^3-2y^2)=5/y-6/(y^3-2y^2)#?

Restrict the domain to prevent division by 0.

Multiply both sides by a factor that eliminates the denominators.

Solve the resulting quadratic equation.

Restrict the domain to prevent division by 0.

Multiply both sides by a factor that eliminates the denominators.

Solve the resulting equation quadratic equation.

Factor:

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To solve the equation (y^2+5y-6)/(y^3-2y^2)=5/y-6/(y^3-2y^2), we can start by simplifying both sides of the equation.

First, we can factor the numerator and denominator of the left side of the equation: (y^2+5y-6)/(y^3-2y^2) = [(y+6)(y-1)] / [y^2(y-2)]

Next, we can factor the numerator and denominator of the right side of the equation: 5/y-6/(y^3-2y^2) = 5/y - [(y-2)(y^2)] / [y^2(y-2)]

Now, we can rewrite the equation with the simplified expressions: [(y+6)(y-1)] / [y^2(y-2)] = 5/y - [(y-2)(y^2)] / [y^2(y-2)]

To eliminate the denominators, we can multiply both sides of the equation by y^2(y-2): (y+6)(y-1) = 5(y-2) - (y-2)(y^2)

Expanding and simplifying the equation: y^2 + 5y - 6 = 5y - 10 - y^3 + 2y^2

Rearranging the terms: y^3 - 2y^2 + y^2 + 5y - 5y + 6 + 10 = 0

Combining like terms: y^3 - y^2 + 16 = 0

This is a cubic equation. To find the solutions, we can use various methods such as factoring, synthetic division, or numerical methods like Newton's method.

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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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