## Find constants k, c so (7x+17)/(x^2+4x+3)=k/(x+3)+c/(x+1)

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Hannah
Posts: 2
Joined: Sun Apr 19, 2009 4:27 pm
Contact:

### Find constants k, c so (7x+17)/(x^2+4x+3)=k/(x+3)+c/(x+1)

I really need help with this problem. I'd appreciate it if somebody would be kind enough of solve it and show me how they did it. Thanks!

Find the constants of k and c so that:

(7x + 17)/(x^2 + 4x + 3) = k/(x + 3) + c/(x + 1)

Sorry about the weird formatting -- I couldn't figure out how to write it any other way. Anyway. good luck!
_______________________________
Edited by stapel --- Reason for edit: Formatting

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
To learn how to format math as text, please review this formatting article. Thank you!
Find the constants of k and c so that:

(7x + 17)/(x^2 + 4x + 3) = k/(x + 3) + c/(x + 1)
Convert the fractions on the right-hand side to the common denominator of (x + 3)(x + 1) = x2 + 4x + 3. Then combine the two fractions. You should end up with:

. . . . .$\frac{7x\, +\, 17}{x^2\, +\, 4x\, +\, 3}\, =\, \frac{(k\, +\, c)x\, +\, (k\, +\, 3c)1}{(x\, +\, 1)(x\, +\, 3)}$

By equating coefficients, you can then set up a system of equations:

. . . . .$\begin{array}{rrrrr}k&+&c&=&7\\k&+&3c&=&17\end{array}$

Solve the system for the values of "k" and "c".