Rational Expression Solution2





Here rational expression solution2 we are going to see solution of some practice questions from the worksheet of multiplying rational fractions.

5. [(3 x² + 2x - 1)/(x² - x - 2)] x [(2 x² - 3 x - 2)/(3 x² + 5 x -2)]

Solution:

Explanation:

We are going to factorize the quadratic equations (3x² + 2x - 1),(x² - x - 2) , (2 x² - 3 x - 2) and (3 x² + 5 x -2)

(3 x² + 2x - 1) = (3 x - 1) (x + 1)

(x² - x - 2) = (x - 2) (x + 1)

(2 x² - 3 x - 2) = (2 x + 1) (x - 2)

(3 x² + 5 x -2) = (2 x - 1) (x + 2)

After cancelling common terms we get (2 x + 1)/(x + 2) as answer.


6. [(2 x - 1)/(x²+2 x+4)] x [(x⁴ - 8 x)/(2 x² + 5 x -3)] x [(x + 3)/(x²- 2x)]

Solution:

Explanation:

By using the algebraic identity (a³ + b³) = (a + b) (a² - a b + b²) we can expand (x³ + 2³) as (x + 2) (x² + 2 x + 4). Now we are going to factorize the quadratic equation (2 x² + 5 x -3)

(2 x² + 5 x -3) = (2 x - 1) (x + 3)

After cancelling common terms we get 1 as answer.


7. [(a + b)/(a - b)] x [(a³ - b³)/(a³ + b³ )]

Solution:

               = [(a + b)/(a - b)] x [(a³ - b³)/(a³ + b³ )

               = [(a + b)/(a - b)] x [(a - b)(a² + ab +b²)/(a + b) (a² - ab + b²)]

               = (a² + ab +b²)/(a² - ab + b²)


8. [(x² - 9 y²)/(3 x - 3y)] x [(x² - y²)/(x² + 4 x y + 3 y²)]

Solution:

            = [(x² - 9 y²)/(3 x - 3y)] x [(x² - y²)/(x² + 4 x y + 3 y²)]

Explanation:

By using the algebraic identity (a²-b²)=(a+b)(a-b) we can expand (x²-(3y)²) as (x + 3y) (x-3y) and expand (x² - y²) as (x+y)(x-y). Now we are going to factorize the equation (x² + 4 x y + 3 y²)

=  x² + 4 x y + 3 y²

=   x² + x y  + 3 x y + 3 y²

=   x (x + y) + 3y (x + y)

=   (x + y) (x + 3y)

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

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