A level partial fractions questionWatch
Here's a link showing the question better. I don't know how to solve for the constants.
Factorise . Divide The numerator by the denominator. This should be enough to find constants Ax + B and the constants Cx + D is the remainder from when you divide the numerator by the denominator.
Update: Yes, person below, multiply both sides by because there isn't an ez way to factorise it.
30x^3 - 26x^2 - 48x + 8 / 3x^2 - 2x - 7} = Ax + B + (Cx+D) / 3x^2 - 2x - 7
The value of should be immediately obvious since the coeff of on the LHS is 30 and on the RHS it will be . These must be equal.
Once you know A, you can easily work out what B is by similar style. What is the coeff of on the LHS ? What is it on the RHS?? Compare them and solve for B.
Then try to get C,D on your own.
P.S. Usually it's a good idea to factorise the denominator , but here you can't do that (nicely) so just follow along with what I've said.
P.S.S. You can also force the RHS into the usual expanded form by expanding it all. Then compare coeffs just by looking at the two sides. However it's useful to snipe out any constants immediately before expanding as that will make your expanding life easier with less algebra involved.