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

Answer 1

Isaiah Anthony

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Answer 2

Eva Adamson

To multiply the given equation, we need to first find a common denominator for both sides. The common denominator is (x-2)(x+3).

Multiplying both sides of the equation by the common denominator, we get:

5(x-2)(x+3) = 2(x-2)(x+3) + (x-3)(x+3)

Expanding and simplifying both sides, we have:

5x^2 + 5x - 10 = 2x^2 + 4x - 4 + x^2 - 9

Combining like terms, we get:

5x^2 + 5x - 10 = 3x^2 + 4x - 13

Rearranging the equation, we have:

5x^2 + 5x - 10 - 3x^2 - 4x + 13 = 0

Simplifying further, we get:

2x^2 + x + 3 = 0

This is a quadratic equation. To solve for x, we can use factoring, completing the square, or the quadratic formula.

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Answer from HIX Tutor

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.