How to Divide a Fractional Algebraic Expression by a Fractional Algebraic Expression (Using the Fractional Bar Form)

Step-by-Step Guide

1. 1

   Step 1: Rewrite the complex fraction as a division problem.

   Remember that a fraction bar means “divided by,” so when you see a fraction over a fraction, you need to divide the top fraction by the bottom fraction.For example, you might see 2x2y−3x4{\displaystyle {\frac {\frac {2x^{2}}{y-3}}{\frac {x}{4}}}}.
   
   You can rewrite this as 2x2y−3÷x4{\displaystyle {\frac {2x^{2}}{y-3}}\div {\frac {x}{4}}}.
2. 2

   Step 2: Take the reciprocal of the second fraction.

   To divide a fraction by a fraction, you take the reciprocal of the second fraction, and you change the division sign to a multiplication sign.
   
   A reciprocal is a fraction in which the numerator and denominator are reversed.For example:2x2y−3÷x4{\displaystyle {\frac {2x^{2}}{y-3}}\div {\frac {x}{4}}}becomes2x2y−3×4x{\displaystyle {\frac {2x^{2}}{y-3}}\times {\frac {4}{x}}} , Use parentheses to show the multiplication, but do not multiply any terms yet.
   
   Writing the expression this way may help you identify terms that can cancel.
   
   For example,2x2y−3×4x=4(2x2)x(y−3){\displaystyle {\frac {2x^{2}}{y-3}}\times {\frac {4}{x}}={\frac {4(2x^{2})}{x(y-3)}}}. , Use the normal rules for simplifying a rational expression to do this.
   
   Cancel out terms common to the numerator and denominator.Remember that you cannot cancel out a single term (like y{\displaystyle y}) from a binomial (like y−3{\displaystyle y-3}).
   
   Also remember that if you have an x2{\displaystyle x^{2}} term in the numerator, and an x{\displaystyle x} term in the denominator, you can cancel out one x{\displaystyle x}, and the x{\displaystyle x} in the denominator disappears, and the x2{\displaystyle x^{2}} in the numerator becomes x{\displaystyle x}.
   
   For example, you can cancel an x{\displaystyle x} in the numerator and denominator in the expression 4(2x2)x(y−3){\displaystyle {\frac {4(2x^{2})}{x(y-3)}}}:4(2x2)x(y−3){\displaystyle {\frac {4(2x^{\cancel {2}})}{{\cancel {x}}(y-3)}}}4(2x)y−3{\displaystyle {\frac {4(2x)}{y-3}}} , If you have any remaining parentheses in the numerator or denominator, simplify these by multiplying.
   
   The result will be your final simplified expression.
   
   For example, 4(2x)y−3=8xy−3{\displaystyle {\frac {4(2x)}{y-3}}={\frac {8x}{y-3}}}.
   
   So, 2x2y−3x4=4(2x)y−3=8xy−3{\displaystyle {\frac {\frac {2x^{2}}{y-3}}{\frac {x}{4}}}={\frac {4(2x)}{y-3}}={\frac {8x}{y-3}}}.
3. 3

   Step 3: Rewrite the expression as a single fraction.

4. 4

   Step 4: Simplify the expression.

5. 5

   Step 5: Complete the necessary multiplications.

Detailed Guide

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