Rational Expression Solution3





Here rational expression solution3 we are going to see solution of some practice questions from the worksheet of multiplying rational fractions.

9. [(x² - 4 x - 12)/(x² - 3 x - 18)] x [(x² - 2 x - 3)/(x² + 3 x + 2)]

Solution:

Explanation:

We are going to factorize the quadratic equations (x² - 4 x - 12) , (x² - 3 x - 18) , (x² - 2 x - 3) and (x² + 3 x + 2)

(x² - 4 x - 12) = (x - 6) (x + 2)

(x² - 3 x - 18) = (x - 6) (x + 3)

(x² - 2 x - 3) = (x - 3) (x + 1)

(x² + 3 x + 2) =  (x + 1) (x + 2)

After cancelling common terms we get (x - 3)/(x + 3) as answer.


10. [(x² - 3x - 10)/(x² - x - 20)] x [(x² - 4 x + 16)/(x³ + 64)]

Solution:

Explanation:

We are going to factorize the quadratic equations (x² - 3x - 10) , (x² - x - 20)

(x² - 3x - 10) = (x - 5) (x + 2)

(x² - x - 20) = (x - 5) (x + 4)

By using the algebraic identity (a³ + b³) = (a + b) (a² - a b + b²) we can expand

(x³ + 4³) = (x + 4) (x² - 4x + 16)

After cancelling common terms we get (x + 2)/(x + 4)² as answer.


11. [(x² - 16)/(x - 2)] x [(x² - 4)/(x³ + 64)]

Solution:

           =   [(x² - 16)/(x - 2)] x [(x² - 4)/(x³ + 64)]

Explanation:

By using the algebraic identity (a²-b²)=(a+b)(a-b) we can expand (x²-4²) as (x + 4) (x - 4) and expand (x² - 2²) as (x + 2)(x - 2). By using the algebraic identity (a³ + b³) = (a + b) (a² - a b + b²) we can expand

After cancelling common terms we get (x - 4)(x + 2)/(x² - 4x + 16) as answer.


12. [(x + 7)/(x² + 14 x + 49)] x [(x²  + 8x + 7)/(x + 1)]

Explanation:

We are going to factorize the quadratic equations (x² + 14 x + 49) , (x²  + 8x + 7)

(x² + 14 x + 49) = (x + 7) (x + 7)

(x²  + 8x + 7) = (x + 1) (x + 7)

After cancelling common terms we get 1 as answer.

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