1. ## Partial fraction again

I got this problem out the multiple choice section in my math book.
It said if $\frac {x+p}{(x-1)(x-3)}\equiv \frac {q}{x-1}+\frac{2}{x-3}$ what are the values of p and q?
Then I got another one that seem to be quite similar if $x^2+4x+p \equiv (x+q)^2+1$ what are the value of p and q? Trying to find two values is what that is confusing to me...

2. The first problem has one equation with 2 variables.

For the second it seems like you should equate coefficents but the information seems to be scarce. Is there any other bits and pieces you can reveal?

3. ## Partial fraction again

sorry I don't have any other information except that.

4. Originally Posted by scrible
I got this problem out the multiple choice section in my math book.
It said if $\frac {x+p}{(x-1)(x-3)}\equiv \frac {q}{x-1}+\frac{2}{x-3}$ what are the values of p and q?
x+p = q(x-3) + 2(x-1)

let x = 1 ...

1+p = -2q

let x = 3 ...

3+p = 4

p = 1 , q = -1

5. Originally Posted by skeeter
x+p = q(x-3) + 2(x-1)

let x = 1 ...

1+p = -2q

let x = 3 ...

3+p = 4

p = 1 , q = -1

Thank you very much, but can you please help me with this one also? if $x^2+4x+p \equiv (x+q)^2+1$ what are the value of p and q? Trying to find two values is what that is confusing to me...

6. Originally Posted by scrible
Thank you very much, but can you please help me with this one also? if $x^2+4x+p \equiv (x+q)^2+1$ what are the value of p and q? Trying to find two values is what that is confusing to me...
Several approaches are possible, including the following:

$x^2 + 4x + p \equiv x^2 + 2qx + q^2 + 1$.

Compare coefficients on each side:

$4 = 2q$ .... (1)

$p = q^2 + 1$ .... (2)

Solve equations (1) and (2) simultaneously.