Partial Fraction `(3x)/(x^2+2x+1)`
Solution:
1. Factors the denominator
`(3x)/(x^2+2x+1)=(3x)/((x+1)^2)`
2. Partial Fraction for each factors
`:. (3x)/((x+1)^2)=A/(x+1)+B/(x+1)^2`
3. Multiply through by the common denominator of `(x+1)^2`
`:. 3x=A(x+1)+B1`
`:. 3x=Ax+A+B`
4. Group the `x`-terms and the constant terms
`:. 3x=Ax+(A+B)`
5. Coefficients of the two polynomials must be equal, so we get equations
`A=3`
`A+B=0`
Solution of equations using Elimination method
Total Equations are `2`
`A+0B=3 -> (1)`
`A+B=0 -> (2)`
Now use back substitution method
From (1)
`A=3`
`=>A=3`
From (2)
`A+B=0`
`=>(3)+B=0`
`=>B+3=0`
`=>B=0-3=-3`
Solution using back substitution method.
`A = 3,B = -3`
After solving these equations, we get
`A=3,B=-3`
Substitute these values in the original fractions
`((3x))/((x+1)^2)=(3)/(x+1)+(-3)/(x+1)^2`
This material is intended as a summary. Use your textbook for detail explanation.
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