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)]** x **[(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.

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