Question

x+6/x^2-3x=A/x+B/x-3 Find A-B

Answer 1

Partial fractions madness!\[\rm {x + 6 \over x^2 - 3x} = {A \over x} + {B \over x - 3}\]

Answer 2

The first thing to do is this:\[\rm {x+6 \over x(x - 3)} = {A \over x} + {B \over x - 3}\]

Answer 3

Now, multiply by the common denominator which is \(\rm x(x - 3)\) (both sides).

Answer 4

\[\rm x + 6 = A(x - 3) + B(x)\]

Answer 5

Now, substitute \(\rm x = -3\) to get the value of \(\rm B\).

Answer 6

And to get the value of \(\rm A\), substitute \(\rm x = 0\).

Answer 7

so B = 3 and A = -2?

Answer 8

A=-2 B=3

Answer 9

No...

Answer 10

Substitute \(\rm x = 3\) to get the value of \(\rm B\).

Answer 11

Yes, so B = 3.

Answer 12

Yeah,
A = -2
B = 3

Answer 13

okay thanks!!

Answer 14

-2 - 3 = -5