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How to divide algebraic fractions

Want to find out how to divide algebraic fractions? We've provided a step-by-step guide of how to divide algebraic fractions to teach you everything you need to know.

Step 1: Find the reciprocal of the divisor

Find the reciprocal of the divisor, which is the fractions after the ÷ symbol. So, if we divide (9x^2)/24y by 5x/(8y^3 ), find the reciprocal of 5x/(8y^3 ) first.

Step 2: Multiply the dividend by the reciprocal

Once the reciprocal of the divisor is determined, multiply the dividend by the reciprocal of the divisor. So, for our example, we multiply (9x^2)/24y by (8y^3)/5x .

Step 3: Simplify the fractions

Look for common factors that can be cancelled to simplify the fractions.

Step 4: Multiply remaining factors

Multiply the remaining factors to find the simplified quotient.

Examples of how to divide algebraic fractions

Q1) Find the quotient of the following algebraic fractions.

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Determine the reciprocal of the divisors (the algebraic fraction after ÷). Hence the following are the reciprocals of the divisor.

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Once we have the reciprocals of the divisors, multiply both dividend and reciprocal.

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Cancel out common factors shared by the numerator and denominator.

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Multiply the remaining the factors to find the quotients. Hence, we have:

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