Solving the equation $\frac{2x+3}{x+1} = \frac{2x+2}{x-1}$ I'm a college student and I've got a problem solving this:
$$\frac{2x+3}{x+1} = \frac{2x+2}{x-1}.$$
Since neither the numerators nor the denominators are equal, I figured that $(2x+3)(x-1) = (x+1)(2x+2)$ would provide me with a suitable $x$.
However calculating this I found that $x = -\frac13$ while my answer sheet states that $x = -\frac23$. What am I doing wrong?

Well you have by cross multiplying that,$$2(x+1)^{2} = 2x^{2} + x -3$$ $$ \Longrightarrow 2x^{2}+4x+2 = 2x^{2} + x -3$$ $$ \Longrightarrow 3x = -5 \Rightarrow x= -\frac{5}{3}$$
