**Multiplication of rational expression :**

Here we are going to see how to multiply two rational expressions.

In the given rational expressions, if we have any quadratic and cubic equation, we have to decompose it into linear factors.

If the given expressions exactly matches with the algebraic identity, we have to factorize them using the appropriate algebraic identities

**Question 1 :**

Multiply the following rational expression into lowest form

[(x² - 2x) /(x + 2)] **⋅ **[(3 x + 6)/(x - 2)]

**Solution :**

**Step 1 :**

By factors out x from x² - 2x, we get x (x - 2)

The numerator of the second fraction is 3x + 6, by factoring out 3 from this, we get 3 (x + 2).

**Step 2 :**

We find the term (x+2) in both numerator and denominator, so we may cancel them.

Like that we find the term (x-2) in both numerator and denominator, so we may cancel them.

**Step 3 : **

The remaining terms are 3 an x.

Hence the answer is 3x.

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

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

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

** x **[(x²-4x+16)/(x²-2x-8)] Solution

5) [(3 x² + 2x - 1)/(x² - x - 2)]

** x **[(2 x² - 3 x - 2)/(3 x² + 5 x -2)] Solution

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

** x **[(x + 3)/(x²- 2x)] Solution

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

8) [(x² - 9 y²)/(3 x - 3y)] **x **

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

9) [(x² - 4 x - 12)/(x² - 3 x - 18)]

** x **[(x² - 2 x - 3)/(x² + 3 x + 2)] Solution

10) [(x² - 3x - 10)/(x² - x - 20)]

** x **[(x² - 4 x + 16)/(x³ + 64)] Solution

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

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

13) [(x² - 5 x + 6 )/(6 x + 6)] **x **[(4 x - 8)/(x² - 4x + 3)]

14. [(p² - 1)/p] **x **[p²/(p - 1)] **x **[1/(p + 1)] Solution

These are the questions in the topic multiplication of rational expression.

- GCD worksheet
- LCM worksheet
- Elimination method worksheet
- Cross multiplication method worksheet
- Equation from roots worksheet
- Synthetic division worksheet
- Factorization worksheet
- Relationship between L.C.M and G.C.D
- Simplifying rational expression

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