partial fractions quick question

why is the partial fractions of x/x+1=a+b/x+1
i dont understand the a

Study Forum Helper

Original post by mikeft

why is the partial fractions of x/x+1=a+b/x+1
i dont understand the a

Because the degree/ order of the numerator is equal to the degree of the denominator.

Original post by mikeft

why is the partial fractions of x/x+1=a+b/x+1
i dont understand the a

You can see why there has to be a constant in there by writing the x on top as x = x + 1 - 1 and then separating the fraction into 2 parts: one with numerator x+1 and the other with numerator -1.

OP

Original post by davros

You can see why there has to be a constant in there by writing the x on top as x = x + 1 - 1 and then separating the fraction into 2 parts: one with numerator x+1 and the other with numerator -1.

got it, it would be the same if i didnt have a variable and i had a number eg 2 2/x+1= the same when having x on the numerator?

Study Forum Helper

Original post by mikeft

got it, it would be the same if i didnt have a variable and i had a number eg 2 2/x+1= the same when having x on the numerator?

No.

\dfrac{1}{x+1} = \dfrac{A}{x+1}

\dfrac{x}{x+1} = A + \dfrac{B}{x+1}

\dfrac{x^2}{x+1} = Ax + B + \dfrac{C}{x+1}

\dfrac{x^3}{x+1} = Ax^2 + B + C + \dfrac{D}{x+1}

etc ...

(edited 11 months ago)

Original post by mikeft

why is the partial fractions of x/x+1=a+b/x+1
i dont understand the a

you just divide x+1 by x and youll get A. When the denominator is the same degree as the numerator you long divide it

(edited 11 months ago)

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