how to solve this maths methods problem

[kj2001]

Absolutely stumped...

Express 2x +1 divided by 5x +3 in the form a divided by x +b    +c

Any help appreciated

[jazzycab]

Absolutely stumped...

Express 2x +1 divided by 5x +3 in the form a divided by x +b    +c

Any help appreciated

I'm assuming what you mean for the answer is that it needs to be in the form \(\frac{a}{x+b}+c\). This can be done in a few ways:
My preferred way of doing this is with a "forced" division. That is, forcing the factor in the denominator to appear in the numerator by multiplying and dividing by the same constant and/or adding and subtracting the same constant:


We could, however, do this using the remainder theorem and equating polynomials:


You could also do this by performing long division (however, I don't know how to get the formatting quite right on the forums for it, so I haven't included it here).

[Sine]

Absolutely stumped...

Express 2x +1 divided by 5x +3 in the form a divided by x +b    +c

Any help appreciated