What is the correct form of the partial fraction decomposition for StartFraction 6 x + 7 Over (x + 2) squared EndFraction? please pick a b c or d below. StartFraction A Over x + 2 EndFraction + StartFraction B Over (x + 2) squared EndFraction

StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over (x + 2) squared EndFraction

StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C Over (x + 2) squared EndFraction

StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C x + D Over (x + 2) squared EndFraction

the answer is d startfraction

answer

When adding or subtracting rational expressions, we combine two or more fractions into a single fraction.

For example:

Add 6/ (x – 5) + (x + 2)/ (x – 5)

Solution

6/ (x – 5) + (x + 2)/ (x – 5) = (6 + x + 2)/ (x -5)

Combine the like terms

= (8 + x)/ (x – 5)

Subtract 4/ (x2 – 9) – 3/ (x2 + 6x + 9)

Solution

Factor the denominator of each fraction to get the LCD.

4/ (x2 – 9) – 3/ (x2 + 6x + 9) ⟹ 4/ (x -3) (x + 3) – 3/ (x + 3) (x + 3)

Multiply each fraction by LCD (x -3) (x + 3) (x + 3) to get;

[4(x + 3) – 3(x – 3)]/ (x -3) (x + 3) (x + 3)

Remove the parentheses in the numerator.

⟹ 4x +12 – 3x + 9/ (x -3) (x + 3) (x + 3)

⟹ x + 21/ (x -3) (x + 3) (x + 3)

In the above two examples, we have combined the fractions into a single fraction by adding and subtracting, now the reverse procedure of adding or subtracting fractions is what is called partial fraction decomposition.

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step-by-step explanation:

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