Partial fraction decomposition for the given expression.

Question

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Answer 1

Question

Chapter C, Problem 1E

To determine

Partial fraction decomposition for the given expression.

Expert Solution & Answer

Answer to Problem 1E

Solution: The required partial fraction decomposition is:

53x(2x+1)=53x−103(2x+1)

Explanation of Solution

Explanation:Given: The expression 53x(2x+1) .

Formula Used: Set up for partial fraction decomposition for the given expression would be of the form:

f(x)(x−a)(x−b)=A(x−a)+B(x−b)

Calculation: We set up the given expression for partial fraction decomposition as shown below:

53x(2x+1)=Ax+B2x+1

Now we need to find the values of A and B that satisfy this equation. This can be done as shown below:

⇒53x( 2x+1)=Ax+B2x+1⇒5=3A(2x+1)+3BxUpon comparing coefficients of all the x terms, we get:⇒3A=5⇒A=53⇒6A+3B=0⇒6(53)+3B=0⇒3B=−10⇒B=−103Thus, the required partial fraction decomposition is:⇒53x( 2x+1)=53x−103( 2x+1)

Conclusion: The given expression has been decomposed using partial fractions and the required decomposition has been found to be 53x(2x+1)=53x−103(2x+1) .

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In simplest terms, Sketch the graph of the parabola. Then, determine its equation. opens downward, vertex is (- 4, 7), passes through point (0, - 39)

Answer 2

Question

Chapter C, Problem 1E

To determine

Partial fraction decomposition for the given expression.

Expert Solution & Answer

Answer to Problem 1E

Solution: The required partial fraction decomposition is:

53x(2x+1)=53x−103(2x+1)

Explanation of Solution

Explanation:Given: The expression 53x(2x+1) .

Formula Used: Set up for partial fraction decomposition for the given expression would be of the form:

f(x)(x−a)(x−b)=A(x−a)+B(x−b)

Calculation: We set up the given expression for partial fraction decomposition as shown below:

53x(2x+1)=Ax+B2x+1

Now we need to find the values of A and B that satisfy this equation. This can be done as shown below:

⇒53x( 2x+1)=Ax+B2x+1⇒5=3A(2x+1)+3BxUpon comparing coefficients of all the x terms, we get:⇒3A=5⇒A=53⇒6A+3B=0⇒6(53)+3B=0⇒3B=−10⇒B=−103Thus, the required partial fraction decomposition is:⇒53x( 2x+1)=53x−103( 2x+1)

Conclusion: The given expression has been decomposed using partial fractions and the required decomposition has been found to be 53x(2x+1)=53x−103(2x+1) .

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Answer 3

Question

Chapter C, Problem 1E

To determine

Partial fraction decomposition for the given expression.

Expert Solution & Answer

Answer to Problem 1E

Solution: The required partial fraction decomposition is:

53x(2x+1)=53x−103(2x+1)

Explanation of Solution

Explanation:Given: The expression 53x(2x+1) .

Formula Used: Set up for partial fraction decomposition for the given expression would be of the form:

f(x)(x−a)(x−b)=A(x−a)+B(x−b)

Calculation: We set up the given expression for partial fraction decomposition as shown below:

53x(2x+1)=Ax+B2x+1

Now we need to find the values of A and B that satisfy this equation. This can be done as shown below:

⇒53x( 2x+1)=Ax+B2x+1⇒5=3A(2x+1)+3BxUpon comparing coefficients of all the x terms, we get:⇒3A=5⇒A=53⇒6A+3B=0⇒6(53)+3B=0⇒3B=−10⇒B=−103Thus, the required partial fraction decomposition is:⇒53x( 2x+1)=53x−103( 2x+1)

Conclusion: The given expression has been decomposed using partial fractions and the required decomposition has been found to be 53x(2x+1)=53x−103(2x+1) .

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Answer 4

Question

Chapter C, Problem 1E

To determine

Partial fraction decomposition for the given expression.

Expert Solution & Answer

Answer to Problem 1E

Solution: The required partial fraction decomposition is:

53x(2x+1)=53x−103(2x+1)

Explanation of Solution

Explanation:Given: The expression 53x(2x+1) .

Formula Used: Set up for partial fraction decomposition for the given expression would be of the form:

f(x)(x−a)(x−b)=A(x−a)+B(x−b)

Calculation: We set up the given expression for partial fraction decomposition as shown below:

53x(2x+1)=Ax+B2x+1

Now we need to find the values of A and B that satisfy this equation. This can be done as shown below:

⇒53x( 2x+1)=Ax+B2x+1⇒5=3A(2x+1)+3BxUpon comparing coefficients of all the x terms, we get:⇒3A=5⇒A=53⇒6A+3B=0⇒6(53)+3B=0⇒3B=−10⇒B=−103Thus, the required partial fraction decomposition is:⇒53x( 2x+1)=53x−103( 2x+1)

Conclusion: The given expression has been decomposed using partial fractions and the required decomposition has been found to be 53x(2x+1)=53x−103(2x+1) .

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Answer 5

Chapter C, Problem 1E

To determine

Partial fraction decomposition for the given expression.

Expert Solution & Answer

Answer to Problem 1E

Solution: The required partial fraction decomposition is:

53x(2x+1)=53x−103(2x+1)

Explanation of Solution

Explanation:Given: The expression 53x(2x+1) .

Formula Used: Set up for partial fraction decomposition for the given expression would be of the form:

f(x)(x−a)(x−b)=A(x−a)+B(x−b)

Calculation: We set up the given expression for partial fraction decomposition as shown below:

53x(2x+1)=Ax+B2x+1

Now we need to find the values of A and B that satisfy this equation. This can be done as shown below:

⇒53x( 2x+1)=Ax+B2x+1⇒5=3A(2x+1)+3BxUpon comparing coefficients of all the x terms, we get:⇒3A=5⇒A=53⇒6A+3B=0⇒6(53)+3B=0⇒3B=−10⇒B=−103Thus, the required partial fraction decomposition is:⇒53x( 2x+1)=53x−103( 2x+1)

Conclusion: The given expression has been decomposed using partial fractions and the required decomposition has been found to be 53x(2x+1)=53x−103(2x+1) .

Answer 6

Chapter C, Problem 1E

To determine

Partial fraction decomposition for the given expression.

Expert Solution & Answer

Answer to Problem 1E

Solution: The required partial fraction decomposition is:

53x(2x+1)=53x−103(2x+1)

Explanation of Solution

Explanation:Given: The expression 53x(2x+1) .

Formula Used: Set up for partial fraction decomposition for the given expression would be of the form:

f(x)(x−a)(x−b)=A(x−a)+B(x−b)

Calculation: We set up the given expression for partial fraction decomposition as shown below:

53x(2x+1)=Ax+B2x+1

Now we need to find the values of A and B that satisfy this equation. This can be done as shown below:

⇒53x( 2x+1)=Ax+B2x+1⇒5=3A(2x+1)+3BxUpon comparing coefficients of all the x terms, we get:⇒3A=5⇒A=53⇒6A+3B=0⇒6(53)+3B=0⇒3B=−10⇒B=−103Thus, the required partial fraction decomposition is:⇒53x( 2x+1)=53x−103( 2x+1)

Conclusion: The given expression has been decomposed using partial fractions and the required decomposition has been found to be 53x(2x+1)=53x−103(2x+1) .

Answer 7

Chapter C, Problem 1E

To determine

Partial fraction decomposition for the given expression.

Answer 8

Expert Solution & Answer

Answer to Problem 1E

Solution: The required partial fraction decomposition is:

53x(2x+1)=53x−103(2x+1)

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Explanation:Given: The expression 53x(2x+1) .

Formula Used: Set up for partial fraction decomposition for the given expression would be of the form:

f(x)(x−a)(x−b)=A(x−a)+B(x−b)

Calculation: We set up the given expression for partial fraction decomposition as shown below:

53x(2x+1)=Ax+B2x+1

Now we need to find the values of A and B that satisfy this equation. This can be done as shown below:

⇒53x( 2x+1)=Ax+B2x+1⇒5=3A(2x+1)+3BxUpon comparing coefficients of all the x terms, we get:⇒3A=5⇒A=53⇒6A+3B=0⇒6(53)+3B=0⇒3B=−10⇒B=−103Thus, the required partial fraction decomposition is:⇒53x( 2x+1)=53x−103( 2x+1)

Conclusion: The given expression has been decomposed using partial fractions and the required decomposition has been found to be 53x(2x+1)=53x−103(2x+1) .