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How to simplify and reduce this to lowest terms

3 Answers

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Multiply numerator and denominator by (x+1)(x+2) then try to factor and cancel.
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2/(x+1) + 1 = ((x+1) + 2)/(x+1) = (x+3)/(x+1)

This is just the numerator. Do the same for the denominator. There should be some opportunity for cancelling.
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So it's:

>((2/(x+1)) + 1) / ((1/(x+2)) + 1).

Start by simplifying the numerator into a single fraction:

* (2/(x+1)) + 1
* (2 + (x+1))/(x+1)
* (x+3)/(x+1)

Do the same for the denominator:

* (1/(x+2)) + 1
* (1 + (x+2))/(x+2)
* (x+3)/(x+2)

Now, note that a fraction is just dividing the numerator by the denominator. And that dividing by something is the same as multiplying by its reciprocal. So dividing something by (x+3)/(x+2) is the same as multiplying by (x+2)/(x+3).

So the fraction simplifies to:

* ((x+3)(x+2))/((x+1)(x+3))

and then we cancel the x+3 factors to get:

* (x+2)/(x+1).

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