The expression p/((x^2)-5x+6) simplifies to (x+4)/(x−2). What expression does p represent?

beljuA

beljuA

Answered question

2021-02-03

The expression p(x2)5x+6 simplifies to x+4x2. What expression does p represent?

Answer & Explanation

Nicole Conner

Nicole Conner

Skilled2021-02-04Added 97 answers

Factoring the denominator of p(x2)5x+6 gives px3(x2).
Since x+4x2 doesn't have a factor of x−3 in the denominator, multiply the numerator and denominator by x−3 so the denominators of both fractions will be the same. Then FOIL in the numerator and denominator:
(x+4)(x3)(x2)(x3)=(x2)3x+4x12(x2)3x2x+6=((x2)+x12)=(x2)+x12(x2)5x+6
Since (x2)+x12(x2)5x+6 must be equal to p(x2)5x+6 , then pp must be the expression (x2)+x12

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