Question

3x/(x-2)(x+1)
into Partial Practions​

Answer 1

Answer:

3x)/(x-2)(x+1)=2/(x-2) + 1/(x+1)

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Step-by-step explanation:

3x/(x-2)(x+1)

Solution:

. Partial fraction for each factors

∴3x/(x-2)(x+1)=A/x-2 + B/x+1

Multiply through by the common denominator of (x-2)(x+1)

∴3x=A×(x+1)+B×(x-2)

∴3x=Ax+A+Bx-2B

Group the x-terms and the constant terms

∴3x=(A+B)x+(A-2B)

Well we get equations

A+B=3

A-2B=0

Total Equations are 2

a+b=3→(1)

a-2b=0→(2)

 Select the equations (1) and (2), and eliminate the variable a.

(a+b=3) - (a-2b)=0

= 3b =3

3b=3

⇒b= 3/3

b=1

From (1)

a+b=3

⇒a+1=3

⇒a=3-1

⇒a=2

After solving these equations, we get

a=2,b=1

Substitute these values in the original fraction

3x/(x-2)(x+1) =2/(x-2) + 1/(x+1)

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