# How do you solve #3-((a-1)/(a+3)) = ((a^2-5)/(a+3))#?

Multiply both sides by

The denominator is the same for both fractions in the equation. We can use this to our advantage by multiplying both sides by the denominator to 'clear' it from our equation:

Now that we've 'cleared' the denominators from the equation, we simplify all the terms:

Now, we have a quadratic equation with the following coefficients:

EDIT: Updating results

Since we have a solution where there's division by zero, this solution is considered extraneous, making it invalid for this question.

This means that the positive root is valid, and gives us our final answer:

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To solve the equation 3-((a-1)/(a+3)) = ((a^2-5)/(a+3)), we can follow these steps:

- Start by multiplying both sides of the equation by (a+3) to eliminate the denominators.
- Simplify the equation by distributing the multiplication on both sides.
- Combine like terms and move all terms to one side of the equation.
- Rearrange the equation to form a quadratic equation.
- Solve the quadratic equation using factoring, completing the square, or the quadratic formula.
- Check the solutions obtained by substituting them back into the original equation to ensure they satisfy the equation.

By following these steps, you can find the solution(s) to the given equation.

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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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