Rational expressions. Solve equations.

Please help me with my homework, I've been solving it from 4 hours and everything is wrong. I just cant get the same answer that the back of the book has.

1. Solve equations.

a)

\frac{x}{3-x}+ 3=\frac{5}{2x-6}

b)

\frac{4}{2x^2+x}- \frac{6x}{2x+1}= 1

2.transform to canonical form

f(x)=\frac{x+3}{x+2}

f(x)=\frac{2x}{x-1}

Re: Rational expressions. Solve equations.

$\displaystyle \frac{x}{3-x} + 3 = \frac{5}{2(x-3)}$

$\displaystyle \frac{-x}{x-3} + 3 = \frac{5}{2(x-3)}$

get a common denominator ...

$\displaystyle \frac{-2x}{2(x-3)} + \frac{3 \cdot 2(x-3)}{2(x-3)} = \frac{5}{2(x-3)}$ ... note that $\displaystyle x \ne 3$ (why?)

all denominators are common, the numerators form the equation

$\displaystyle -2x + 6(x-3) = 5$

finish it.