OpenStudy (anonymous):

help with partial fractions

7 years ago
OpenStudy (anonymous):
7 years ago

myininaya (myininaya):

\[\frac{9x^2+19x+56}{x(x-8)(x-7)}=\frac{A}{x}+\frac{B}{x-8}+\frac{C}{x-7}\] =\[\frac{A(x-8)(x-7)+Bx(x-7)+Cx(x-8)}{x(x-8)(x-7)}\] since the denominators are the same then the numerators are the same \[9x^2+19x+56=A(x-8)(x-7)+Bx(x-7)+Cx(x-8)\] \[9x^2+19x+56=A(x^2-15x+56)+B(x^2-7x)+C(x^2-8x)\]

7 years ago
myininaya (myininaya):

\[9x^2+19x+56=Ax^2+Bx^2+Cx^2-15Ax-7Bx-8Cx+56A\] \[9x^2+19x+56=x^2(A+B+C)+x(-15A-7B-8C)+56A\]

7 years ago
myininaya (myininaya):

so A+B+C=9 -15A-7B-8C=19 56A=56

7 years ago
myininaya (myininaya):

so 56A=56 implies A=1 so we have 1+B+C=9 and -15-7B-8C=19

7 years ago
myininaya (myininaya):

B+C=8 and -7B-8C=34 B=8-C -7(8-C)-8C=34 -56+7C-8C=34 -C=90 C=-90 B=8-(-90)=8+90=98

7 years ago
myininaya (myininaya):

A=1, B=98, C=-90 A/x+B/(x-8)+C/(x-7)=1/x+98/(x-8)-90/(x-7)

7 years ago
myininaya (myininaya):

i didn't do on scratch paper there may be a mistake above but if you look at what i was trying to do you should be able to figure how to do this problem and get the right answer you can also check my if you want by combining the partial fractions

7 years ago