# How do you solve the differential #dy/dx=(x+1)/(x^2+2x-3)^2#?

# y = -1/(2(x^2+2x-3)) + c#

Is a First Order Separable Differential Equation, so we can just separate the variables;

The LHS is immediately integrable, and for the RHS we use the substitution;

Which gives:

And now we can integrate to get;

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To solve the differential equation ( \frac{dy}{dx} = \frac{x + 1}{(x^2 + 2x - 3)^2} ), integrate both sides with respect to ( x ). This type of equation may require partial fraction decomposition to integrate.

After performing the necessary algebraic manipulations, the solution to the differential equation will be obtained.

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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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