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Калькулятор розкладання звичайних дробів

Крок за кроком знаходимо звичайні дроби

Цей онлайн калькулятор знайде розкладання раціональної функції на часткові дроби з покроковим поясненням.

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Solution

Your input: perform the partial fraction decomposition of x+7x2+3x+2

Simplify the expression: x+7x2+3x+2=x+7(x+1)(x+2)

The form of the partial fraction decomposition is

x+7(x+1)(x+2)=Ax+1+Bx+2

Write the right-hand side as a single fraction:

x+7(x+1)(x+2)=(x+1)B+(x+2)A(x+1)(x+2)

The denominators are equal, so we require the equality of the numerators:

x+7=(x+1)B+(x+2)A

Expand the right-hand side:

x+7=xA+xB+2A+B

Collect up the like terms:

x+7=x(A+B)+2A+B

The coefficients near the like terms should be equal, so the following system is obtained:

{A+B=12A+B=7

Solving it (for steps, see system of equations calculator), we get that A=6, B=5

Therefore,

x+7(x+1)(x+2)=6x+1+5x+2

Answer: x+7x2+3x+2=6x+1+5x+2