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Find each product or quotient.

3b12b+4÷b26b+8

Short Answer

Expert verified

The simplified expression is 3b2+2b8.

Step by step solution

01

Step 1. Define the concept.

Multiplying rational expression: - Let a, b, c, and d be polynomials withb0 and d0. Then abcd=acbd.

Dividing rational expression: - Let a, b, c, and d be polynomials with b0,c0 and d0. Then ab÷cd=abdc=adbc.

02

Step 2. Multiply by the reciprocal of b2−6b+8.

First multiply by the reciprocal of b26b+8and then factor the expressions in numerator and denominator.

role="math" localid="1648050245885" 3b12b+4÷b26b+8=3b12b+4×1b26b+8=3b4b+4×1b4b2

03

Step 3. Simplify the expression.

Further simplify the expression by cancelling out the common factors b4.

role="math" localid="1648050393663" 3b12b+4÷b26b+8=3b4b+4×1b4b2=3b+4b2=3b2+2b8

Therefore, the simplified expression is role="math" localid="1648050403311" 3b2+2b8.

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