What is the correct form of the partial fraction decomposition for the expression StartFraction 13 x minus 7 Over (x + 2) (4 x minus 3) EndFraction?

StartFraction A Over x + 2 EndFraction + StartFraction B Over 4 x minus 3 EndFraction
StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over 4 x minus 3 EndFraction
StartFraction A Over (x + 2) (4 x minus 3) EndFraction + StartFraction B Over (x + 2) (4 x minus 3) EndFraction
StartFraction A Over (x + 2) (4 x minus 3) EndFraction + StartFraction B x + C Over (x + 2) (4 x minus 3) EndFraction

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Mathematics

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What is the correct form of the partial fraction decomposition for the expression StartFraction 13 x minus 7 Over (x + 2) (4 x minus 3) EndFraction?

StartFraction A Over x + 2 EndFraction + StartFraction B Over 4 x minus 3 EndFraction
StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over 4 x minus 3 EndFraction
StartFraction A Over (x + 2) (4 x minus 3) EndFraction + StartFraction B Over (x + 2) (4 x minus 3) EndFraction
StartFraction A Over (x + 2) (4 x minus 3) EndFraction + StartFraction B x + C Over (x + 2) (4 x minus 3) EndFraction

$What is the correct form of the partial fraction decomposition for the expression StartFraction 13 x minus 7 Over (x + 2) (4 x minus 3) EndFraction? StartFracti class=$

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AFOKE88 AFOKE88 · Answer 1 · 2025-03-31T13:44:48-04:00

The correct form of the partial fraction decomposition for the expression (13x - 7)/((x + 2)(4x - 3)) is;

Option B; [A/(x + 2)] + [(Bx + C)/(4x - 3)]

The given complex fraction is;

(13x - 7)/((x + 2)(4x - 3))

Now partial fractions are simply decomposition of complex fractions into simpler fractions. For example we want to decompose the complex fraction;

4/[(x - 1)(x + 5)]

The right format will be;

[A/(x - 1)] + [B/(x + 5)]

Applying this same pattern above to our question, we can decompose the fraction (13x - 7)/((x + 2)(4x - 3)) into;

[A/(x + 2)] + [(Bx + C)/(4x - 3)]

In conclusion, the correct answer is Option B.

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shubhamchouhanvrVT shubhamchouhanvrVT · Answer 2 · 2025-03-31T13:44:02-04:00

The correct form of the partial fraction decomposition for the expression (13x - 7)/((x + 2)(4x - 3)) is; Option B; [tex]\dfrac{A}{(x + 2)} +\dfrac{Bx + C)}{(4x - 3)}[/tex]

What is a function?

A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

The given complex fraction is;

(13x - 7)/((x + 2)(4x - 3))

Now partial fractions are simply the decomposition of complex fractions into simpler fractions. For example, we want to decompose the complex fraction;

4/[(x - 1)(x + 5)]

The right format will be;

[A/(x - 1)] + [B/(x + 5)]

Applying this same pattern above to our question, we can decompose the fraction (13x - 7)/((x + 2)(4x - 3)) into;

[A/(x + 2)] + [(Bx + C)/(4x - 3)]

In conclusion, the correct answer is Option B.

To know more about fractions follow

brainly.com/question/12587229

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