# Year 13 Maths Partial fractions: Repeated Linear factors

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4x²+16x+15/(x+1)(x+2)²= A/(x+1) + B/(x+2)¹ + C/(x+2)²

My questions is that why is it this

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1)

and not this

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1) (x+2)

I'm not sure where the extra (x+2), i've been told you cancel out the (x+2)² with a (x+2)² leaving just (x+1) but why does that happen?

Sorry if this question is bad, first time posting lol

My questions is that why is it this

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1)

and not this

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1) (x+2)

I'm not sure where the extra (x+2), i've been told you cancel out the (x+2)² with a (x+2)² leaving just (x+1) but why does that happen?

Sorry if this question is bad, first time posting lol

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(Original post by

4x²+16x+15/(x+1)(x+2)²= A/(x+1) + B/(x+2)¹ + C/(x+2)²

My questions is that why is it this

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1)

and not this

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1) (x+2)

I'm not sure where the extra (x+2), i've been told you cancel out the (x+2)² with a (x+2)² leaving just (x+1) but why does that happen?

Sorry if this question is bad, first time posting lol

**EdBedd**)4x²+16x+15/(x+1)(x+2)²= A/(x+1) + B/(x+2)¹ + C/(x+2)²

My questions is that why is it this

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1)

and not this

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1) (x+2)

I'm not sure where the extra (x+2), i've been told you cancel out the (x+2)² with a (x+2)² leaving just (x+1) but why does that happen?

Sorry if this question is bad, first time posting lol

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1) makes sense because C has (x+2)^2, so it only needs to be multiplied by (x+1). (I also can't read the indices, since the font is too small.)

If you take the example of x =1:

A/(x+1) + B/(x+2)¹ + C/(x+2)² = A/2 + B/3 + C/9

You would need A(9) + B(6) + C(2) in order to put it all over 18 in the fraction. C(6) would mess up the values in the equation.

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(Original post by

In partial fractions, you're multiplying the numerator with the factor missing from the denominator.

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1) makes sense because C has (x+2)^2, so it only needs to be multiplied by (x+1). (I also can't read the indices, since the font is too small.)

If you take the example of x =1:

A/(x+1) + B/(x+2)¹ + C/(x+2)² = A/2 + B/3 + C/9

You would need A(9) + B(6) + C(2) in order to put it all over 18 in the fraction. C(6) would mess up the values in the equation.

**MindMax2000**)In partial fractions, you're multiplying the numerator with the factor missing from the denominator.

4x²+16x+15= A(x+2)² + B(x+1)(x+2) + C(x+1) makes sense because C has (x+2)^2, so it only needs to be multiplied by (x+1). (I also can't read the indices, since the font is too small.)

If you take the example of x =1:

A/(x+1) + B/(x+2)¹ + C/(x+2)² = A/2 + B/3 + C/9

You would need A(9) + B(6) + C(2) in order to put it all over 18 in the fraction. C(6) would mess up the values in the equation.

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