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