Divide (8x-5)/(2x+1)

Problem

(8*x−5)/(2*x+1)

Solution

1. Identify the goal to perform polynomial long division or synthetic division on the rational expression.

2. Divide the leading term of the numerator 8*x by the leading term of the denominator 2*x to find the first term of the quotient.

8*x/2*x=4

3. Multiply the entire divisor 2*x+1 by the quotient term 4

4*(2*x+1)=8*x+4

4. Subtract this result from the original numerator to find the remainder.

(8*x−5)−(8*x+4)=−9

5. Express the result in the form Quotient+Remainder/Divisor

4+(−9)/(2*x+1)

Final Answer

(8*x−5)/(2*x+1)=4−9/(2*x+1)

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