# Division of Rational Expressions

## Key Questions

• Division of a rational expression are similar to fractions.For dividing rational expressions, you will use the same method as you used for dividing numerical fractions: when dividing by a fraction, you flip-n-multiply. For instance:

[ (x^2 + 2x - 15) / (x^2 - 4x - 45) ] ÷ [ (x^2 + x - 12) / (x^2 - 5x - 36) ]

here as you see i have factored the different expressions and cancelled the common expression finally it gets reduced to nothing

Hope this helped you

• Multiplication

$\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$

Division

$\frac{a}{b} \div i \mathrm{de} \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} = \frac{a \cdot d}{b \cdot c}$

I hope that this was helpful.

• Remember that dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction, that is,

$\frac{a}{b} \div i \mathrm{de} \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} = \frac{a \cdot d}{b \cdot c}$

I hope that this was helpful.

• I would just turn it into multiplications.

$\frac{a}{b} \div i \mathrm{de} \frac{c}{d} \div i \mathrm{de} \frac{e}{f} = \frac{a}{b} \times \frac{d}{c} \times \frac{f}{e} = \frac{a \cdot d \cdot f}{b \cdot c \cdot e}$

I hope that this was helpful.

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