Question

7X^2 +2 all over (2x+1)(x^2 +1)

Answer 1

what about it?

Answer 2

i got A/2x+1 + Bx+C/(X^2+1)

Answer 3

is that right? because of the x^2

Answer 4

this one is easier

Answer 5

i figure out A = 3

Answer 6

no. factors in denominator are only
\[(2x+1)(x^2+1)\]

Answer 7

x is not a factor of the denominator

Answer 8

oh no that is not right sorry

Answer 9

B = 2?

Answer 10

harder, not easier. because
\[x^2+1\] has degree = 2, you need
\[\frac{Ax+B}{x^2+1}+\frac{C}{2x+1}\]

Answer 11

i led you astray. because the denominator has degree 2, the numerator can have degree 1

Answer 12

so this one is harder

Answer 13

you have
\[(Ax+B)(2x+1)+c(x^2+1)=7x^2+2\]

Answer 14

now you have to multiply out and equate like coefficients. you get
\[2Ax^2+Ax+2Bx+B+Cx^2+C=7x^2+2\]

Answer 15

oh ok thats the step i miss

Answer 16

now collect terms on the left. i hope i didn't screw this up.
you get
\[(2A+C)x^2+(A+2B)x+(B+C)=7x^2+2\]

Answer 17

giving the following equations by "equating like coefficients"
\[2A+C=7\]
\[A+2B=0\]\[B+C=2\]

Answer 18

hope it is clear where i got those from

Answer 19

what did you do?

Answer 20

first step was to collect terms. that is for powers of x

Answer 21

\[2Ax^2+Cx^2=(2A+C)x^2\] for example
that is on the left. on the right you have
\[7x^2\] so you know that
\[2A+C=7\]

Answer 22

likewise
\[Ax+2Bx=(A+2B)x\] on the left, and you have no x term on the right, so you know
\[A+2B=0\]

Answer 23

oh ok

Answer 24

and finally the "constant" on the left is \[B+C\] and on the right it is 2 giving
\[B+C=2\]

Answer 25

now your job is to solve this system of equations. 3 equations, 3 unknowns

Answer 26

may ways but i will say this:
second equation gives
\[A=-2B\]put that in first equation you get
\[-4B+C=7\]
\[B+C=2\] subtract to get
\[-5B=5\] so
\[B=-1\]

Answer 27

now it is easy, since
\[B+C=2\]
\[-1+C=2\]
\[C=3\]

Answer 28

\[2A+C=7\]\[2A+3=7\]
\[2A=4\]
\[A=2\]

Answer 29

problem cooked up with nice integer solutions. as you can imagine it is usually not so simple at the last step

Answer 30

hahhaa thank you soo much!