What is the right choice for question 18? http://postimage.org/image/k4z2s8lkx/

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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The problem 18 requests to find the common denominator for the expression `(x+4)/(x^2-3x) + (x+5)/(x^2 - x - 6)`

Notice that you may factor out x in the denominator `x^2-3x ` such that:

`x^2-3x = x(x - 3)`

You should substitute 3 for x in denominator `x^2 - x - 6`  to verify if 3 is a zero for this denominator such that:

`3^2 - 3 - 6 = 9 - 3 - 6 = 0`

Notice that the next zero of `x^2 - x - 6`  is `-2` , hence, you may wriite the factored form of this denominator such that:

`x^2 - x - 6 = (x - 3)(x + 2)`

You need to rewrite the denominators of the given fractions such that:

`(x+4)/(x(x - 3)) + (x+5)/((x - 3)(x + 2))`

Notice that the common denominator of the fractions is `x(x - 3)(x + 2), ` hence, you should multiply the first fraction by `x+2`  and the second fraction by x such that:

`((x+2)(x+4) + x(x+5))/(x(x - 3)(x + 2)) `

Hence, evaluating the common denominator of these fractions yields `x(x - 3)(x + 2)` , hence, you need to select the third answer. 

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