**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

After having gone through the stuff given above, we hope that the students would have understood "Multiplication of rational expression".

If you want to know more about the stuff "Multiplication of rational expression" Please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**