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Find the quotient.

x+32x+6÷3x64x8

Short Answer

Expert verified

The final answer is 23.

Step by step solution

01

Step 1. Define a rational function.

A function of the form y=pq is called a rational function, where p and q are the polynomials and q0.

02

Step 2. Define the quotient of two expressions ab and cd.

The quotient of two expressions aband cd, where b0and d0, is given below.

ab÷cd=ab×dc=acbd           ...........(1)

03

Step 3. Calculate the quotient x+32x+6÷3x−64x−8.

Use (1) to find the quotient x+32x+6÷3x64x8.

x+32x+6÷3x64x8=x+32x+6×4x83x6=(x+3)(4x8)(2x+6)(3x6)=(x+3)4(x2)2(x+3)3(x2)=23

Therefore, the final answer is 23.

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