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# ​ Simplify the expression

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Simplify the expression Feb 7, 2018

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Simplify the following:

(x^2 + 3 x - 28)/(x^2 - 7 x + 12)

Factor x^2 - 7 x + 12 by finding two numbers whose product is 12 and whose sum is -7.

The factors of 12 that sum to -7 are -3 and -4. So, x^2 - 7 x + 12 = (x - 3) (x - 4):

(x^2 + 3 x - 28)/((x - 3) (x - 4))

Factor x^2 + 3 x - 28 by finding two numbers whose product is -28 and whose sum is 3.

The factors of -28 that sum to 3 are 7 and -4. So, x^2 + 3 x - 28 = (x + 7) (x - 4):

((x + 7) (x - 4))/((x - 3) (x - 4))

Cancel common terms in the numerator and denominator of ((x + 7) (x - 4))/((x - 3) (x - 4)).

((x + 7) (x - 4))/((x - 3) (x - 4)) = (x - 4)/(x - 4)×(x + 7)/(x - 3) = (x + 7)/(x - 3):

=(x + 7) / (x - 3)

Feb 7, 2018

#1
0

Simplify the following:

(x^2 + 3 x - 28)/(x^2 - 7 x + 12)

Factor x^2 - 7 x + 12 by finding two numbers whose product is 12 and whose sum is -7.

The factors of 12 that sum to -7 are -3 and -4. So, x^2 - 7 x + 12 = (x - 3) (x - 4):

(x^2 + 3 x - 28)/((x - 3) (x - 4))

Factor x^2 + 3 x - 28 by finding two numbers whose product is -28 and whose sum is 3.

The factors of -28 that sum to 3 are 7 and -4. So, x^2 + 3 x - 28 = (x + 7) (x - 4):

((x + 7) (x - 4))/((x - 3) (x - 4))

Cancel common terms in the numerator and denominator of ((x + 7) (x - 4))/((x - 3) (x - 4)).

((x + 7) (x - 4))/((x - 3) (x - 4)) = (x - 4)/(x - 4)×(x + 7)/(x - 3) = (x + 7)/(x - 3):

=(x + 7) / (x - 3)

Guest Feb 7, 2018