Rational Expression Solution1





Here rational expression solution1 we are going to see solution of some practice questions from the worksheet of multiplying rational fractions.

Multiply the following rational expression into lowest form

1. [(x² - 2x) /(x + 2)] x [(3 x + 6)/(x - 2)]

Solution:

Explanation:

In the first step we have taken x commonly from numerator of the first rational fraction and we have taken 3 as common from the second rational fraction.After cancelling common terms from the numerator and denominator we get 3x as answer.


2. [(x² - 81)/(x² - 4)] x [(x² + 6 x + 8)/(x² - 5 x - 36)]

Solution:

Explanation:

By using the algebraic identity a² - b² = (a + b) (a - b) we can expand x² - 9² as (x + 9) (x - 9) and we can expand x² - 2² as (x + 2) (x - 2). Now we are going to factorize the quadratic equations (x² + 6 x + 8) (x² - 5 x - 36).

(x² + 6 x + 8) = (x + 2) (x + 4)

(x² - 5 x - 36) = (x - 9) (x + 4)

After cancelling common terms we get (x + 9)/(x - 2) as answer.


3. [(x² - 3 x - 10)/(x² - x - 20)] x [(x² - 2 x + 4)/(x³ + 8)]

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 equations (x² - 3 x - 10) and (x² - x - 20).

(x² - 3 x - 10) = (x - 5) (x + 2)

(x² - x - 20) = (x - 5) (x + 4)

After cancelling common terms we get 1/(x + 4) as answer.


4. [(x²-16)/(x²-3x+2)] x [(x²-4)/(x³+64)][(x²-4x+16)/(x²-2x-8)]

Solution:            rational expression solution1 rational expression solution1

Explanation:

(a² - b²) = (a + b) (a -  b)

(x² - 4²) = (x + 4) (x -  4)

(x² - 2²) = (x + 2) (x -  2)

(a³ + b³) = (a + b) (a² - a b + b²)

(x³ + 4³) = (x + 4) (x² - 4 x + 16)

Now we are going to factorize the quadratic equations (x² - 3 x + 2) and (x² -2 x - 8)

(x² - 3 x + 2) = (x - 1) (x - 2)

(x² -2 x - 8) = (x - 4) (x + 2)

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