Write the rational expression in simplest form. (x^2-9)/(x^3+x^2-9x-9). and the second question is perform the multiplication or division and simplyfy (x^2-36)/x divided by (x^3-6x^2)/(x^2+x).

Maia Pace

Maia Pace

Answered question

2022-08-04

Write the rational expression in simplest form. x 2 9 / x 3 + x 2 9 x 9. and the second question is perform the multiplication or division and simplyfy x 2 36 / x divided by x 3 6 x 2 / x 2 + x.

Answer & Explanation

quillassed7

quillassed7

Beginner2022-08-05Added 13 answers

Write the rational expression in simplest form.
x 2 9 / x 3 + x 2 9 x 9
( x 2 9 ) / ( x 3 + x 2 9 x 9 )
= ( x 2 9 ) / [ x 2 ( x + 1 ) 9 ( x + 1 ) ]
= ( x 2 9 ) / [ ( x + 1 ) ( x 2 9 ) ]
= 1/(x+1)
Answer: 1/(x+1)
Filipinacws

Filipinacws

Beginner2022-08-06Added 2 answers

When you have a rational expression, try to factor the numerator(top) and denominator (bottom) so that you can cancel out terms.For my answer, I reverse-FOILed the numerator, and used synthetic division to factor the denominator (twice) in order to come to my conclusion.
( x 2 9 ) / ( x 3 + x 2 9 x 9 )
= ( x + 3 ) ( x 3 ) / ( x + 3 ) ( x 2 2 x 3 )
= ( x 3 ) / ( x 2 2 x 3 )
= (x-3)/(x-3)(x+1)
= 1/(x+1)

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