Dividing by a Rational Expression
Master Dividing by a Rational Expression in Grade 10 math. To divide by a rational expression, you multiply the first expression by the reciprocal of the secon.
Key Concepts
To divide by a rational expression, you multiply the first expression by the reciprocal of the second one. This method is often called 'keep, change, flip.' The rule is formally stated as: $$ \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} $$, where the denominators b, c, and d cannot be equal to zero.
Example 1: $$ \frac{15x^4}{2y^2} \div \frac{3x^2}{8y^3} = \frac{15x^4}{2y^2} \cdot \frac{8y^3}{3x^2} = \frac{120x^4y^3}{6x^2y^2} = 20x^2y $$ Example 2: $$ \frac{x+3}{x 8} \div \frac{x(x+3)}{x 8} = \frac{x+3}{x 8} \cdot \frac{x 8}{x(x+3)} = \frac{1}{x} $$.
Division is just multiplication in a clever disguise. Remember the 'keep, change, flip' rule: keep the first fraction, change division to multiplication, and flip the second fraction (its reciprocal). After this quick change, you simply follow the multiplication rules. Factor all the numerators and denominators completely, then cancel any common factors to find your simplified answer.
Common Questions
What is Dividing by a Rational Expression?
To divide by a rational expression, you multiply the first expression by the reciprocal of the second one. This method is often called 'keep, change, flip.' The rule is formally stated as: terms, everything is gone. - Step 4: The final simplified answer is 1. Common mistake tip: A very common...
How do you apply Dividing by a Rational Expression in practice?
Example 1: $$
Why is Dividing by a Rational Expression important for Grade 10 students?
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