Question: PLAY
To divide rational algebraic expressions remember the procedures in dividing like getting the
reciprocal of the divisors and changing the division sign to multiplication sign. Then multiply
numerator to numerator and denominator to denominator.
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FIND THE QUOTIENT OF THE FOLLOWING RATIONAL ALGEBRAIC EXPRESSION: ANSWER IN 1
WHOLE PAD PAPER.
1. $$\frac{81x^{3}z}{36y} \div \frac{27x^{2}z^{2}}{12xy}$$
2. $$\frac{2a+2b}{a^{2}+ab} \div a$$
3. $$\frac{3x^{2}}{10y} \div \frac{12xy}{5y^{2}}$$
4. $$\frac{x}{4} \div \frac{x^{2}}{8}$$
5. $$\frac{n^{2}-9}{n} \div \frac{n+3}{n}$$
6. $$\frac{5x-25}{2x} \div \frac{4x-20}{1}$$
7. $$\frac{y^{2}-36}{y+6} \div \frac{y^{2}-49}{y+7}$$
8. $$\frac{n^{2}-6n+9}{n-3} \div \frac{n^{2}-9}{n+3}$$
9. $$\frac{ad}{bc} \div \frac{ab}{b}$$
10. $$\frac{a-3}{a+1}$$
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1. **Problem:** Find the quotient of $$\frac{81x^{3}z}{36y} \div \frac{27x^{2}z^{2}}{12xy}$$.
2. **Formula:** Dividing rational expressions means multiplying by the reciprocal:
$$\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \times \frac{D}{C}$$.
3. **Apply formula:**
$$\frac{81x^{3}z}{36y} \times \frac{12xy}{27x^{2}z^{2}}$$
4. **Multiply numerators and denominators:**
$$\frac{81x^{3}z \times 12xy}{36y \times 27x^{2}z^{2}} = \frac{972x^{4}y z}{972x^{2}y z^{2}}$$
5. **Simplify numerator and denominator:**
Cancel common factors:
$$\frac{\cancel{972}x^{4} \cancel{y} z}{\cancel{972}x^{2} \cancel{y} z^{2}} = \frac{x^{4} z}{x^{2} z^{2}}$$
6. **Simplify powers:**
$$x^{4} \div x^{2} = x^{4-2} = x^{2}$$
$$z \div z^{2} = z^{1-2} = z^{-1} = \frac{1}{z}$$
7. **Final simplified quotient:**
$$\frac{x^{2}}{z}$$
**Answer:** $$\frac{x^{2}}{z}$$